A royal family has children until it has a boy or until it has three children, whichever comes first. Assume that each child is a boy with probability 1/2. Find the expected number of boys in this royal family and the expected number of boys.
References
Doyle, Peter G. (2006). "Grinstead and Snell's Introduction to Probability" (PDF). Retrieved June 6, 2024.
Solution: C
The number of boys say [math]N[/math] is less than equal to 1. The probability that there are no boys only occurs when we have 3 girls and this equals (1/2)3. Hence the expected number of boys equals 1-0.125 = 0.875.