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.

Question

A tent Matches
Desert 1 5
Rainforest 2 4
What is the probability that a randomly selected participant spun the first wheel and landed on rainforest and spun the second wheel and landed on a tent?
Simplify any fractions.

Answer 1

To determine the probability that a randomly selected participant landed on "rainforest" on the first wheel and "tent" on the second wheel, we will first analyze each spin separately and then combine the probabilities.

Step 1: Determine the total outcomes for each wheel.

First Wheel (Location) Outcomes:

1. Desert
2. Rainforest

Total outcomes for the first wheel = 2.

Second Wheel (Bonus Survival Tool) Outcomes:

1. Tent
2. Matches

Total outcomes for the second wheel = 2.

Step 2: Calculate Individual Probabilities.

Probability of landing on Rainforest: \[ P(\text{Rainforest}) = \frac{\text{Number of outcomes for Rainforest}}{\text{Total outcomes for the first wheel}} = \frac{1}{2} \]

Probability of landing on Tent: \[ P(\text{Tent}) = \frac{\text{Number of outcomes for Tent}}{\text{Total outcomes for the second wheel}} = \frac{1}{2} \]

Step 3: Combine the Probabilities.

The events are independent, so we multiply the probabilities together: \[ P(\text{Rainforest and Tent}) = P(\text{Rainforest}) \times P(\text{Tent}) = \frac{1}{2} \times \frac{1}{2} = \frac{1}{4} \]

Conclusion

The probability that a randomly selected participant spun the first wheel and landed on "rainforest" and spun the second wheel and landed on "tent" is: \[ \boxed{\frac{1}{4}} \]