Question

Theoretical Probabilites. Use the theoretical method to determine the probability of the following outcomes and events. State any assumptions that you make.

1.)Randomly selecting a two- child family with two boys

2.)Randomly selecting a three-child family with exactly two boys

Answer 1

1) Zet . x is a brandom variable X = No. of boys in a two-child family Here. X~ Bin (n. 6) where = 2 p= { [ probability of getting a boy Probability of getting two boys in a two-child family is a child canbe P[ X = 27 a boy or gért M 22 (₂) ² (²) 2-2 - 4 = 0.25 2) Let y be a random variable defined as, 4: No. of Joeys in a thou - child fassily Here, y ~ Bin (0,6), where = 3 p = 12 [as a child a boy Selecting exactly Now, Probability Can be a of three - Child family with girl two boys = Pty=2 3 c2 () ² () 3-2 0.375