A couple plans to have children unti they get a girt, but they agree they will n

Question

A couple plans to have children unti they get a girt, but they agree they will not have more than three children, even f all are boys Assume thal the probabity of having a ger a) Create a probability model for the number of children they'll have. b) Find the expected number of children. c) Find the expected number of boys they' have 2 2499 2601 (Round to four decimal places as needed.) b)E00-1.7701 Round to four decimal places as needed ) ) E(number of boys)- Round the final answer to four decimal places as needed Round all intermediate values to four decimal places as needed) nter your answer in the answer box and then click Check Answer Clear All l parts showing

Explanation / Answer

a) Here first the number of boys for each case is computed as: Let the number of boys be Y. Then,

P(Y=0) = 0.49, P(Y=1) = 0.2499 P(Y=2) = 0.512*0.49 = 0.127449 and P(Y=3) = 0.513 = 0.132651

Therefore the expected number of boys in the family is computed as:

= 0*0.49 + 1*0.2499 + 2*0.127449 + 3*0.132651

= 0.9028

Therefore 0.9028 is the required expected number of boys here.

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