could someone show me how to do part b step by step please? 4. The probability t

ID: 3218134 • Letter: C

Question

could someone show me how to do part b step by step please?

4. The probability that any child in a certain family will have blue eyes is 1/4, and this feature is inherited independently by different children in the family. Suppose there are five children in the family. a) If it is known that at least one of these children has blue eyes, what is the probability that at least three of the children have blue eyes? b) If it is known that the youngest child in the family has blue eyes, what is the probability that at least three of the children have blue eyes?

Explanation / Answer

Part b)

as probability of having x blue eyed children, P(x)=ncx p^x(1-p)^n-x

From above

p(x)

CDF P(x)

0.2373

0.3955

0.6328

0.2637

0.8965

0.0879

0.9844

0.0146

0.9990

0.0010

1.0000

For youngest to have blue eyes ,probability =1/4

hence probability =P(3<=X<=5)/(1/4)

==(0.0879+0.0146+0.0010) /(1/4)

=0.414