I only need an answer to the last question about the boys an

I only need an answer to the last question about the boys and girls the options are:

0.120, 0.128, 0.135 or 0.127

Attempts: Do No Harm: /2 3. Using probability rules to compute the probabilities of dependent events Aa Aa A typical deck of playing cards contains 52 cards, with 13 cards of each suit. Suppose you have an incomplete deck with only 24 cards, but it does contain all 13 hearts. If you randomly draw four cards (without replacement), the probability that all four cards are hearts is 0.06729 A couple plans to have three children. After doing some research, they learn that the probability their first child will be a girl is 0.49, and the probability of having a boy is 1 minus 0.49, or 0.51. In addition, having a girl increases the probability that the next child will be a girl by 0.03, while having a boy decreases by 0.02 the probability of having a girl next. Using this information, the probability they will have three children in the following order: boy-girl-girl (a boy and two girls) is p(girl) + p(boy) = 1, or p(girl) = 1-p(boy) and p(boy) = 1-p(girl).) . (Hint: Remember to assume that each child will always be a girl or a boy. That is,

Solution

Four cards are drawn without replacement from an incomplete deck of 24 cards which contain 13hearts.

Thus the probability that all 4 cards are hearts is:

(13/24)*(12/23)*(11/22)*(10/21)

=0.06729

The probability of having the first boy is 0.51.

By the given information if the first child is a boy then the probability of having a girl next is 0.49-0.02=0.47.

Again, the probability of having a girl again after the birth of a girl is 0.49+0.03=0.52

Thus the probability of having 3 children in an order boy-girl-girl is: 0.51*0.47*0.52=0.125