F.5 MATHS probability

yan

2010-12-05 4:35 pm

1.The probability that Kelly passes a Chinese test is 1/2 .
The probability that she passes a Mathematics test is 3/5 .
Assume that her results of these two subjects are independent.

(a)Find the probability that Kelly passes at least one of the two tests.
(b)Given that Kelly passes at least one of the two tests, find the probability that she passes the Mathematics test.

2.Among the 12 players in a basketball team A, 3 players are from Red house, 4 players are from Ylow house and 5 players are from Green house.

Among the 9 players in a basketball team B, 2 players are from Red house, 3 players are from Yellow house and 4 players are from Blue house. If a player is chosen at random from each team, find the probability that

(a)the two players chosen belong to the same house,
(b)the two players chosen belong to different houses.

識做一題都幫我做下~

回答 (1)

不用客氣

2010-12-05 5:44 pm

✔ 最佳答案

1.(a)
P(pass at least one test)
= 1 - P(fail in both two tests)
= 1 - (1 - 1/2) x (1 - 3/5)
= 1 - (1/2) x (2/5)
= 1 - 1/5
= 4/5

1.(b)
P(pass Math test | pass at least one test)
= (3/5) / (4/5)
= 3/4

2.(a)
P(two players belong to the same house)
= P(Red, Red) + P(Yellow, Yellow) + P(Green, Green)
= (3/12) x (2/9) + (4/12) x (3/9) + (5/12) x (4/9)
= 6/108 + 12/108 + 20/108
= 38/108
= 19/54

2(b)
P(two players belong to different houses)
= 1 - P(two players belong to the same house)
= 1 - 19/54
= 35/54

參考: micatkie

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