Question

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 a sibling? Enter your response as a decimal (1 point)

Left: Pets = 0:35
Middle = 0.11
Right: Siblings = 0.43
Outside of the diagram right = 0.11

Answer 1

To find the probability that a child has a pet or a sibling, we need to apply the principle of inclusion-exclusion.

From the Venn diagram we have:
- Probability of having a pet (P(Pet)) = 0.35
- Probability of having a sibling (P(Sibling)) = 0.43
- Probability of having both a pet and a sibling (P(Pet ∩ Sibling)) = 0.11

According to the principle of inclusion-exclusion, the probability of having a pet or a sibling (P(Pet ∪ Sibling)) is given by the formula:

\[
P(Pet ∪ Sibling) = P(Pet) + P(Sibling) - P(Pet ∩ Sibling)
\]

Substituting the values, we get:

\[
P(Pet ∪ Sibling) = 0.35 + 0.43 - 0.11
\]

Calculating this:

\[
P(Pet ∪ Sibling) = 0.35 + 0.43 = 0.78
\]
\[
P(Pet ∪ Sibling) = 0.78 - 0.11 = 0.67
\]

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