Question

Genetics says that children receive genes from each of their parents independently. Each child of a particular pair of parents has probability 0.25 of having type O blood. Suppose these parents have five children. Let X = the number of children with type O blood

1. Is this Experiment a binomial setting? Explain?

2. Find the probability that the exactly four of the children have type O blood?

c. Find the probability that at least one child has type O blood [P(X ≥1) =?]

d. Find the Expected value (the mean) and the standard deviation of the random variable X?

Answer 1

a) This is a binomial experiment

There experiment has a well defines success and failure with a constant success rate. The probability of a child having O type blood is independent of the blood group of other children.

Number of trials n, = 5

P(success), p = 0.25

q = 1 - p = 0.75

P(X) = nCx p^x q^n-x

b) P(exactly four of the children have type O blood), P(X = 4) = 5C4 x 0.25⁴ x 0.75

= 0.01465

c) P(at least one child has type O blood), P(X 1) = 1 - P(0)

= 1 - 0.75⁵

= 0.7627

d) Expected value = np

= 5 x 0.25

= 1.25

Standard deviation =

=

= 0.9682