I have this problem which I am having trouble figuring out, can anyone walk me through it?
A survey of families with two children is conducted. The probability of both children being girls is 25%.
(1) Find the probability that at least two out of three families will have two girls. I found the answer to be P(GG) = 1/4 / P(GB,BG,GG) = 3/4 or 1/3 chance of having two girls given the first is a girl. Then I took 1/3 * 1/3 * 2/3 = .074 + 1/3 * 1/3 * 1/3 = .037 for a .11 chance of two out of three families having 2 girls.
I'm not sure if the above is correct.
(2) In a survey of 100 families, find the expected value and standard deviation of the number of families with two girls.
I'm a loss at this one. I know Expected Value = The Sum of (Xi * P(Xi)) and after that I know how to find the standard deviation I just don't know how to figure this one out given the 100 families.
(3) Using the normal approximation to binomial distrubution, find the probability that less than 20 out of 100 families have two girls.
Once again I know binomial mean and Std. Dev is Ux = np and std dev of x = sq rt of (np(1-p)
anyone help me please?
A survey of families with two children is conducted. The probability of both children being girls is 25%.
(1) Find the probability that at least two out of three families will have two girls. I found the answer to be P(GG) = 1/4 / P(GB,BG,GG) = 3/4 or 1/3 chance of having two girls given the first is a girl. Then I took 1/3 * 1/3 * 2/3 = .074 + 1/3 * 1/3 * 1/3 = .037 for a .11 chance of two out of three families having 2 girls.
I'm not sure if the above is correct.
(2) In a survey of 100 families, find the expected value and standard deviation of the number of families with two girls.
I'm a loss at this one. I know Expected Value = The Sum of (Xi * P(Xi)) and after that I know how to find the standard deviation I just don't know how to figure this one out given the 100 families.
(3) Using the normal approximation to binomial distrubution, find the probability that less than 20 out of 100 families have two girls.
Once again I know binomial mean and Std. Dev is Ux = np and std dev of x = sq rt of (np(1-p)
anyone help me please?