Question

Pets
0.35
Both
0.11
Siblings
0.43

0.11


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 either a pet or a sibling (or both), we can use the principle of inclusion-exclusion for the probabilities. The formula is as follows:

\[
P(\text{Pets} \cup \text{Siblings}) = P(\text{Pets}) + P(\text{Siblings}) - P(\text{Both})
\]

From your data:
- \( P(\text{Pets}) = 0.35 \)
- \( P(\text{Siblings}) = 0.43 \)
- \( P(\text{Both}) = 0.11 \)

Now, substitute these values into the formula:

\[
P(\text{Pets} \cup \text{Siblings}) = 0.35 + 0.43 - 0.11
\]

Calculating:

\[
P(\text{Pets} \cup \text{Siblings}) = 0.35 + 0.43 = 0.78
\]
\[
P(\text{Pets} \cup \text{Siblings}) = 0.78 - 0.11 = 0.67
\]

Therefore, the probability that the child has a pet or a sibling is \( \boxed{0.67} \).