Final answer:
The question asks for the conditional probability of visitors buying 3D theater tickets given they bought planetarium tickets. Calculation shows it's approximately 46.15%, which rounds to 46%. The closest provided answer option is 52%.
Step-by-step explanation:
The student is asking about the conditional probability, specifically what percent of museum visitors buy tickets for the 3D theater given that they have already bought tickets for the planetarium.
To find this, we need to use the following equation:
P(A|B) = P(A and B) / P(B)
Where:
- P(A|B) is the probability of event A occurring given that B has occurred.
- P(A and B) is the probability of both events A and B occurring.
- P(B) is the probability of event B occurring.
From the question, we have:
- P(Planetarium and 3D Theater) = 24% or 0.24
- P(Planetarium) = 52% or 0.52
Using the equation we get:
P(3D Theater | Planetarium) = P(Planetarium and 3D Theater) / P(Planetarium)
= 0.24 / 0.52
≈ 0.4615 or 46.15%
After rounding, the nearest percent is 46%, which is not one of the options provided. However, the closest answer from the options given would be 52%, option (a).