probability (5) 20點

2007-11-06 8:14 am

Suppose that, in a large population , a family is selected at random from among those that have three children . Further suppose that genders in successive births are independent and that the probability of a female child is p. Let Y denote the number of female children in the family obtained.
a)Obtain the PMF of the random variable Y.

更新1:

Use the FPF and part (a) to determine the probability that the number of female children in the family obtained is b) exactly one. c) at most one. d) at least one.

回答 (2)

魏王將張遼

2007-11-07 12:37 am

✔ 最佳答案

(a) Using "M" and "F" for indicating male and female children, we have, for a family having 3 children, the possible sequences of the genders of the children are:

MMM
MMF
MFM
FMM
MFF
FMF
FFM
FFF
Therefore, counting all the above possibilites, we can construct the Probability Mass Function as follows:
P(X) = 1/8, if X = 0 or 3
P(X) = 3/8, if X = 1 or 2
P(X) = 0, otherwise.
(b) From the result of (a), the probability that exactly one female child is 3/8.
(c) From the result of (a), the probability that at most one female child is 1/8 + 3/8 = 1/2.
(d) From the result of (a), the probability that at least one female child is 1 - 1/8 = 7/8.

參考: My Maths knowledge

👍 0 👎 0

用戶25975

2007-11-11 6:30 am

........

👍 0 👎 0