Question

Pets
0.35
Both
0.11
Siblings
0.43



The Venn diagram displays the probability that a particular child in Mr. Brown's class has a pet or a sibling, or both . What is the probability that the child has a pet or sibling? Enter your response as a decimal.

The probability that the child has a pet or a sibling is ___

Answer 1

To find the probability that a child has a pet or a sibling, we can use the principle of inclusion-exclusion for probabilities.

Let:
- \( P(A) \) = probability of having a pet = 0.35
- \( P(B) \) = probability of having a sibling = 0.43
- \( P(A \cap B) \) = probability of having both a pet and a sibling = 0.11

We want to find \( P(A \cup B) \), the probability of having a pet or a sibling (or both). The formula for this is:

\[
P(A \cup B) = P(A) + P(B) - P(A \cap B)
\]

Now, substituting the values:

\[
P(A \cup B) = 0.35 + 0.43 - 0.11
\]

Calculating this step-by-step:

1. \( 0.35 + 0.43 = 0.78 \)
2. \( 0.78 - 0.11 = 0.67 \)

So, the probability that the child has a pet or a sibling is \( 0.67 \).

Therefore, the final answer is:

The probability that the child has a pet or sibling is **0.67**.