On a reality show, contestants had to spin two wheels of fate. Spinning the first wheel determined the remote location where contestants would reside for the duration of the season. Spinning the second wheel determined which "bonus survival tool" they would be allowed to bring, along with a few other necessary items.A tent MatchesDesert 2 5Rainforest 7 5What is the probability that a randomly selected participant spun the first wheel and landed on rainforest given that the participant spun the second wheel and landed on matches?Simplify any fractions.
Question
On a reality show, contestants had to spin two wheels of fate. Spinning the first wheel determined the remote location where contestants would reside for the duration of the season. Spinning the second wheel determined which "bonus survival tool" they would be allowed to bring, along with a few other necessary items.A tent MatchesDesert 2 5Rainforest 7 5What is the probability that a randomly selected participant spun the first wheel and landed on rainforest given that the participant spun the second wheel and landed on matches?Simplify any fractions.
Solution
To solve this problem, we need to use the concept of conditional probability. The formula for conditional probability is P(A|B) = P(A ∩ B) / P(B). In this case, event A is landing on "rainforest" and event B is landing on "matches".
From the table, we can see that the total number of outcomes for the first wheel is 2 (Desert and Rainforest) and for the second wheel is 10 (5 for Matches and 5 for Tent).
The number of outcomes where both A and B occur (A ∩ B) is 5 (Rainforest and Matches).
The number of outcomes where B occurs is 5 (Matches).
So, the probability that a randomly selected participant spun the first wheel and landed on rainforest given that the participant spun the second wheel and landed on matches is:
P(A|B) = P(A ∩ B) / P(B) = 5 / 5 = 1.
So, the probability is 1, or 100%. This means that if a participant landed on matches, they definitely landed on rainforest.
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