Question

Match each statement to the appropriate probability rule that can be used to determine the required information:

"The probability of a couple having three girls out of five offspring?"

A) Addition Rule
B) Multiplication Rule
C) Binomial Probability Formula
D) Conditional Probability

Answer 1

The probability of a couple having three girls out of five offspring can be determined using the Binomial Probability Formula (C). Plugging in the values into the formula, we calculate the probability to be 0.3125.

correct option is C) Binomial Probability Formula

Step-by-step explanation:

The probability of a couple having three girls out of five offspring can be determined using the Binomial Probability Formula (C).

1. First, we need to identify the values needed for the binomial probability formula. The number of trials is 5 (the couple having 5 offspring) and the probability of success (having a girl) is 0.5 (assuming equal probability of having a boy or a girl).
2. Next, we can use the binomial probability formula: P(X=k) = C(n,k) * p^k * (1-p)^(n-k). In this case, k=3 (three girls), n=5 (five offspring), and p=0.5 (probability of having a girl).
3. Plugging in the values, we get P(X=3) = C(5,3) * 0.5^3 * (1-0.5)^(5-3).
4. Simplifying the expression, we find P(X=3) = 10 * 0.125 * 0.25 = 0.3125.

Therefore, the probability of a couple having three girls out of five offspring is 0.3125, which can be calculated using the binomial probability formula.