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)

Question

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.