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.

1 answer

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.