Question

question 14
a couple plans to have four children. using a tree diagram, obtain the sample space. then, find the probability that the family has at least one boy.
a 13/16
b 1
c 13/4
d 15/16
5 points

Explanation:

Step1: Calculate the probability of no boys

The probability of having a girl each time is $\frac{1}{2}$. For four children, the probability of all - girls (no boys) is $(\frac{1}{2})^4=\frac{1}{16}$.

Step2: Use the complement rule

The probability of at least one boy is the complement of the probability of no boys. Let \(P(X\geq1)\) be the probability of at least one boy and \(P(X = 0)\) be the probability of no boys.
By the formula \(P(X\geq1)=1 - P(X = 0)\)
Substitute \(P(X = 0)=\frac{1}{16}\) into the formula, we get \(P(X\geq1)=1-\frac{1}{16}=\frac{16 - 1}{16}=\frac{15}{16}\)

Answer:

D. \(15/16\)