Maths: Probability

2009-07-31 1:36 am

1. In a class of 40 students, 25 of them are members of Maths. Club
and 28 of them are members of Sports Club.(Every student must join
at least one of the two club.)
(a.) How many student are members of both clubs? (Ans: 13)
(b). Find the probability that a student randomly selected from the
class is not member of Sport Club.(Ans: 3/10)
(c). If 2 students, who originally join the Sports Club only, also join
the Maths Club, what is the probability that a student randomly
selected from the class joins one club?(Ans: 5/8)

2. Find the expected values of the following:
(a). Tossing a fair die with six faces. (Ans: 5/21)
(b). A man draw a note randomly from 5 notes with values: 1 note
of $20, 2 notes of $50, 1 note of $100 and 1 note of $500.(Ans:475)
(c). If two babies were born, the number of boy.(Ans:3/10)

回答 (1)

用戶2053

2009-08-01 7:44 am

✔ 最佳答案

1a) 25 + 28 - 40 = 13 student are members of both clubs.
b) The probability of a student is a member of Sport Club = 28/40
So the probability that a student randomly selected from the
class is not member of Sport Club = 1 - 28/40 = 3/10
c) In this case , 13+2 = 15 student are members of both clubs ,
the probability of a student is NOT joins one club = 15/40
So the probability that a student randomly selected from the class joins one club = 1 - 15/40 = 5/8
2a) expected value
= (1 + 2 + 3 + 4 + 5 + 6) * 1/6 = 7/2 ( is not 5/21?)
2b) expected value
= 20 * 1/5 + 50 * 2/5 + 100 * 1/5 + 500 * 1/5
= 144 ( is not 475 ?)
2c) expected value
= P(2 boys)*2 + P(2 girls)*0 + P(boy & girl)*1 + P(girl & boy)*1
= (1/2)^2 * 2 + (1/2)^2 * 0 + (1/2)^2 * 1 + (1/2)^2 * 1
= 1/2 + 0 + 1/4 + 1/4
= 1 ( is not 3/10 ?)

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