Question

Adrenaline Rush is an arcade and family fun center. The probability that a visitor will purchase a game of laser tag is 0.43. The probability that a visitor will purchase a game of laser tag and a go-kart ticket is 0.39.
Jim buys a game of laser tag at Adrenaline Rush. What is the probability that he also buys a go-kart ticket?
Write your answer as a decimal rounded to the nearest hundredth.

Answer 1

To find the probability that Jim buys a go-kart ticket given that he has already purchased a game of laser tag, we can use the concept of conditional probability.

Let:
- \( A \) be the event that a visitor purchases a game of laser tag.
- \( B \) be the event that a visitor purchases a go-kart ticket.

From the information given:
- \( P(A) = 0.43 \) (the probability that a visitor purchases a game of laser tag)
- \( P(A \cap B) = 0.39 \) (the probability that a visitor purchases both a game of laser tag and a go-kart ticket)

We want to find \( P(B | A) \), the probability that a visitor purchases a go-kart ticket given that they have purchased a game of laser tag. This can be calculated using the formula for conditional probability:

\[
P(B | A) = \frac{P(A \cap B)}{P(A)}
\]

Substituting the known values:

\[
P(B | A) = \frac{0.39}{0.43}
\]

Calculating \( \frac{0.39}{0.43} \):

\[
P(B | A) \approx 0.90697674
\]

Rounding this to the nearest hundredth:

\[
P(B | A) \approx 0.91
\]

Thus, the probability that Jim also buys a go-kart ticket, given that he has purchased a game of laser tag, is **0.91**.