{"id":4640,"date":"2016-05-17T11:49:00","date_gmt":"2016-05-17T06:19:00","guid":{"rendered":"http:\/\/mycbseguide.com\/blog\/ncert-solutions-class-11-maths-exercise-16-2\/"},"modified":"2016-05-17T13:42:52","modified_gmt":"2016-05-17T08:12:52","slug":"ncert-solutions-class-11-maths-exercise-16-2","status":"publish","type":"post","link":"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-11-maths-exercise-16-2\/","title":{"rendered":"NCERT Solutions class-11 Maths Exercise 16.2"},"content":{"rendered":"

Exercise 16.2<\/strong><\/p>\n

1. A die is rolled. Let E be the event \u201cdie shows 4\u201d and F be the event \u201cdie shows even number\u201d. Are E and F mutually exclusive?<\/strong><\/p>\n

Ans. <\/strong>When a die is rolled, then S = {1, 2, 3, 4, 5, 6}<\/p>\n

E: die shows 4 = {4} and F: die shows even number = {2, 4, 6}<\/p>\n

Now, E F = {4} <\/p>\n

Therefore, E and F are not mutually exclusive events.<\/p>\n

\n

2. A die is thrown. Describe the following events.<\/strong><\/p>\n

(i) A: a number less than 7 <\/strong><\/p>\n

(ii) B: a number greater than 7<\/strong><\/p>\n

(iii) C: a multiple of 3<\/strong><\/p>\n

(iv) D: a number less than 4<\/strong><\/p>\n

(v) E: an even number greater than 4 <\/strong><\/p>\n

(vi) F: a number not less than 3<\/strong><\/p>\n

Ans. <\/strong>When a die is thrown, then S = {1, 2, 3, 4, 5, 6}<\/p>\n

(i) <\/strong>A: a number less than 7 = {1, 2, 3, 4, 5, 6}<\/p>\n

(ii) <\/strong>B: a number greater than 7 = <\/p>\n

(iii) <\/strong>C: a multiple of 3 = {3, 6}<\/p>\n

(iv) <\/strong>D: a number less than 4 = {1, 2, 3}<\/p>\n

(v) <\/strong>E: an even number greater than 4 = {6}<\/p>\n

(vi) <\/strong>F: a number not less than 3 = {3, 4, 5, 6}<\/p>\n

AB = {1, 2, 3, 4, 5, 6} AB = <\/p>\n

BC = {3, 6}EF = {6}<\/p>\n

DE = A \u2013 C = {1, 2, 4, 5}<\/p>\n

D \u2013 E = {1, 2, 3}EF\u2019 = <\/p>\n

F\u2019 = {1, 2}<\/p>\n

\n

3. An experiment involves rolling a pair of dice and recording the numbers the numbers that come up. Describe the following events:<\/strong><\/p>\n

A: the sum is greater than 8<\/strong><\/p>\n

B: 2 occurs on either die<\/strong><\/p>\n

C: the sum is at least 7 and a multiple of 3<\/strong><\/p>\n

Which pairs of these events are mutually exclusive?<\/strong><\/p>\n

Ans. <\/strong>When a pair of die is rolling then<\/p>\n

S = {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6)<\/p>\n

(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6)<\/p>\n

(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6)<\/p>\n

(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6)<\/p>\n

(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6)<\/p>\n

(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}<\/p>\n

A:<\/strong> the sum is greater than 8 = {(3, 6), (4, 5), (5, 4), (6, 3), (4, 6), (5, 5), (6, 4), (5, 6), (6, 5), (6, 6)}<\/p>\n

B:<\/strong> 2 occurs on either die = {(1, 2), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 2), (4, 2), (5, 2),<\/p>\n

(6, 2)}<\/p>\n

C:<\/strong> the sum is at least 7 and a multiple of 3 = {(3, 6), (6, 3), (5, 4), (4, 5), (6, 6)}<\/p>\n

AB = therefore, A and B are mutually exclusive events.<\/p>\n

BC = therefore, B and C are mutually exclusive events.<\/p>\n

AC = {(3, 6), (6, 3), (5, 4), (4, 5), (6, 6)} <\/p>\n

therefore, A and C are not mutually exclusive events.<\/p>\n

\n

4. Three coins are tossed once. Let A denotes the event \u201cthree heads show\u201d, B denotes the event \u201ctwo heads and one tail show\u201d, C denotes the event \u201cthree tails show\u201d and D denotes the event \u201ca head shows on the first coin\u201d. Which events are (i) mutually exclusive, (ii) simple, (iii) compound?<\/strong><\/p>\n

Ans. <\/strong>When three coins are tossed then S = {HHH, HHT, HTH, THH, TTH, HTT, TTT}<\/p>\n

A:<\/strong> three heads shows = {HHH}<\/p>\n

B:<\/strong> two heads and one tail show = {HHT, HTH, THH}<\/p>\n

C:<\/strong> three tails show = {TTT}<\/p>\n

D:<\/strong> a head shows on the first coin = {HHH, HHT, HTH, HTT}<\/p>\n

(i) <\/strong>AB = therefore, A and B are mutually exclusive events.<\/p>\n

BC = therefore, B and C are mutually exclusive events.<\/p>\n

AD = {HHH} therefore, A and D are not mutually exclusive events.<\/p>\n

BD = {HHT, HTH} therefore, B and D are not mutually exclusive events.<\/p>\n

CD = therefore, C and D are mutually exclusive events.<\/p>\n

(ii) <\/strong>A = {HHH}, Here therefore, A is a simple event.<\/p>\n

C = {TTT}, Here therefore, C is a simple event.<\/p>\n

(iii) <\/strong>B = {HHT, HTH, THH}, Here therefore, B is a compound event.<\/p>\n

D = {HHH, HHT, HTH, HTT} Here therefore, B is a compound event.<\/p>\n

\n

5. Three coins are tossed. Describe:<\/strong><\/p>\n

(i) Two events which are mutually exclusive.<\/strong><\/p>\n

(ii) Three events which are mutually exclusive and exhaustive.<\/strong><\/p>\n

(iii) Two events, which are not mutually exclusive.<\/strong><\/p>\n

(iv) Two events which are mutually exclusive but not exhaustive.<\/strong><\/p>\n

(v) Three events which are mutually exclusive but not exhaustive.<\/strong><\/p>\n

Ans. <\/strong>When three coins are tossed then S = {HHH, HHT, HTH, THH, TTH, HTT, TTT}<\/p>\n

(i) <\/strong>A: getting at least two heads = {HHH, HHT, HTH, THH}<\/p>\n

B: getting at least two tails = {HTT, THT, TTH, TTT}<\/p>\n

AB = therefore, A and B are mutually exclusive events.<\/p>\n

(ii) <\/strong>A: getting at least two heads = {HHH, HHT, HTH, THH}<\/p>\n

B: getting exactly one head = {HTT, THT, TTH}<\/p>\n

C: getting no head = {TTT}<\/p>\n

AB = therefore, A and B are mutually exclusive events.<\/p>\n

BC = therefore, B and C are mutually exclusive events.<\/p>\n

AC = therefore, A and C are mutually exclusive events.<\/p>\n

Also ABC = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT} = S<\/p>\n

Therefore, A, B, C are mutually exclusive events.<\/p>\n

(iii) <\/strong>A: getting at least two heads = {HHH, HHT, HTH, THH}<\/p>\n

B: getting exactly two heads = {HHT, HTH, THH}<\/p>\n

AB = {HHT, HTH, THH} <\/p>\n

Therefore, A and B are not mutually exclusive events.<\/p>\n

(iv) <\/strong>A: getting three heads = {HHH}<\/p>\n

B: getting three tails = {TTT}<\/p>\n

AB = therefore, A and B are mutually exclusive events.<\/p>\n

AB = {HHH, TTT} S therefore, A and B are not exhaustive.<\/p>\n

(v) <\/strong>A: getting three heads = {HHH}<\/p>\n

B: getting exactly two heads = {HHT, HTH, THH}<\/p>\n

C: getting three tails = {TTT}<\/p>\n

AB = therefore, A and B are mutually exclusive events.<\/p>\n

BC = therefore, B and C are mutually exclusive events.<\/p>\n

AC = therefore, A and C are mutually exclusive events.<\/p>\n

Also ABC = {HHH, HHT, HTH, THH, TTT} S<\/p>\n

Therefore, A, B, C are not mutually exclusive events.<\/p>\n

\n

6. Two dice are thrown. The events A, B and C are as follows:<\/strong><\/p>\n

A: getting an even number on the first die<\/strong><\/p>\n

B: getting an odd number on the first die<\/strong><\/p>\n

C: getting the sum of the numbers on the dice 5<\/strong><\/p>\n

Describe the events:<\/strong><\/p>\n

(i) A\u2019 <\/strong><\/p>\n

(ii) not B <\/strong><\/p>\n

(iii) A or B <\/strong><\/p>\n

(iv) A and B<\/strong><\/p>\n

(v) A but not C <\/strong><\/p>\n

(vi) B or C <\/strong><\/p>\n

(vii) B and C <\/strong><\/p>\n

(viii) A B\u2019 C\u2019<\/strong><\/p>\n

Ans. <\/strong>When two dice are thrown, then<\/p>\n

S = {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6)<\/p>\n

(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6)<\/p>\n

(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6)<\/p>\n

(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6)<\/p>\n

(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6)<\/p>\n

(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}<\/p>\n

A: getting an even number on the first die<\/p>\n

= {(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (4, 1),<\/p>\n

(4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}<\/p>\n

B: getting an odd number on the first die<\/p>\n

= {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (3, 1), (3, 2),<\/p>\n

(3, 3), (3, 4), (3, 5), (3, 6), (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6)}<\/p>\n

C: getting the sum of the number on the dice<\/p>\n

5 = {(1, 1), (1, 2), (1, 3), (1, 4), (2, 1), (2, 2),<\/p>\n

(2, 3), (3, 1), (3, 2), (4, 1)}<\/p>\n

(i) <\/strong>A\u2019 = {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (5, 1),<\/p>\n

(5, 2), (5, 3), (5, 4), (5, 5), (5, 6)} = B<\/p>\n

(ii) <\/strong>not B = {(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6),<\/p>\n

(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)} = A<\/p>\n

(iii) <\/strong>A or B = {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6)<\/p>\n

(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6)<\/p>\n

(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6)<\/p>\n

(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6)<\/p>\n

(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6)<\/p>\n

(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)} = S<\/p>\n

(iv) <\/strong>A and B = AB = <\/p>\n

(v) <\/strong>A but not C = A \u2013 C = {(2, 4), (2, 5), (2, 6), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (6, 1), (6, 2),<\/p>\n

(6, 3), (6, 4), (6, 5), (6, 6)}<\/p>\n

(vi) <\/strong>B or C = BC = {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2),<\/p>\n

(3, 3), (3, 4), (3, 5), (3, 6), (4, 1), (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6)<\/p>\n

(vii) <\/strong>B and C = BC = {(1, 1), (1, 2), (1, 3), (1, 4), (3, 1), (3, 2)}<\/p>\n

(viii) <\/strong>AB\u2019C\u2019 = {(2, 4), (2, 5), (2, 6), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (6, 1), (6, 2), (6, 3),<\/p>\n

(6, 4), (6, 5), (6, 6)}<\/p>\n

\n

7. Refer to question 6 above, state true or false (give reason for your answer):<\/strong><\/p>\n

(i) A and B are mutually exclusive.<\/strong><\/p>\n

(ii) A and B are mutually exclusive and exhaustive.<\/strong><\/p>\n

(iii) A = B\u2019<\/strong><\/p>\n

Ans. <\/strong>A: getting an even number on the first die<\/p>\n

= {(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (4, 1),<\/p>\n

(4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}<\/p>\n

B: getting an odd number on the first die<\/p>\n

= {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (3, 1), (3, 2),<\/p>\n

(3, 3), (3, 4), (3, 5), (3, 6), (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6)}<\/p>\n

C: getting the sum of the number on the dice<\/p>\n

5 = {(1, 1), (1, 2), (1, 3), (1, 4), (2, 1), (2, 2),<\/p>\n

(2, 3), (3, 1), (3, 2), (4, 1)}<\/p>\n

(i) <\/strong>AB = therefore, A and B are mutually exclusive events. True<\/p>\n

(ii) <\/strong>AB = and AB = S<\/p>\n

Therefore, A and B are mutually exclusive and exhaustive events. True<\/p>\n

(iii) <\/strong>B\u2019 = {(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6),<\/p>\n

(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6),<\/p>\n

(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)} = A True<\/p>\n

(iv) <\/strong>AC = {(2, 1), (2, 2), (2, 3), (4, 1)} = <\/p>\n

Therefore, A and C are not mutually exclusive events. False<\/p>\n

(v) <\/strong>AB\u2019 = A Therefore, A and B\u2019 are not mutually exclusive events. False<\/p>\n

(vi) <\/strong>Since A\u2019 = B and B\u2019 = A, AB = , BC = {(1, 1), (1, 2), (1, 3), (1, 4), (3, 1), (3, 2) <\/p>\n

AC = {(2, 1), (2, 2), (2, 3), (4, 1)} = <\/p>\n

Therefore, A\u2019, B\u2019 and C are not mutually exclusive. False<\/p>\n","protected":false},"excerpt":{"rendered":"

Exercise 16.2 1. A die is rolled. Let E be the event \u201cdie shows 4\u201d and F be the event \u201cdie shows even number\u201d. Are E and F mutually exclusive? Ans. When a die is rolled, then S = {1, 2, 3, 4, 5, 6} E: die shows 4 = {4} and F: die shows … Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[47,281],"tags":[],"class_list":["post-4640","post","type-post","status-publish","format-standard","hentry","category-cbse-class-11","category-ncert-solutions"],"yoast_head":"\nNCERT Solutions class-11 Maths Exercise 16.2 | myCBSEguide<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-11-maths-exercise-16-2\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"NCERT Solutions class-11 Maths Exercise 16.2 | myCBSEguide\" \/>\n<meta property=\"og:description\" content=\"Exercise 16.2 1. A die is rolled. Let E be the event \u201cdie shows 4\u201d and F be the event \u201cdie shows even number\u201d. Are E and F mutually exclusive? Ans. When a die is rolled, then S = {1, 2, 3, 4, 5, 6} E: die shows 4 = {4} and F: die shows ... 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