Question

Suppose P( male birth )=0.48. A couple wishes to have exactly three daughters in the mily and will continue having children until this happens. Let X be the number of is family has.

The random variable X has a negative binomial distribution with parameters where a suçcess is __

Answer 1

The random variable X represents the number of children a couple has until they have exactly three daughters. The probability of having no children is 0.

Step-by-step explanation:

The random variable X represents the number of children a couple has until they have exactly three daughters. This is an example of a negative binomial distribution. In this case, a success is defined as the birth of a daughter. The probability of a success (P) is given as 0.48.

To find the distribution of X, we use the negative binomial formula: P(X=k) = (k-1)C(r-1) * P^r * (1-P)^(k-r), where k is the number of trials, r is the desired number of successes, and P is the probability of success. In this case, r=3 and P=0.48.

To find the probability that the couple has no children, we use the formula P(X=0) = (0-1)C(3-1) * 0.48^3 * (1-0.48)^(0-3). However, since the couple wants to have at least three daughters, the probability of having no children is 0.