Question

A wheel used on a game show has 12 spaces total; 8 spaces with dollar amounts written on them and 4 spaces with “Lose a Turn” written on them. All of the spaces on the wheel are equal in size. If a contestant on this show spins the wheel 3 times, find the probability that the contestant spins “Lose a Turn” all three times.

Answer 1

The probability that a contestant will land on 'Lose a Turn' all three times when spinning the wheel is calculated by multiplying the probability of 'Lose a Turn' occurring in a single spin, which is 1/3, three times. The final result is 1/27, rounded to four decimal places, gives a probability of 0.0370 or 3.70%.

Step-by-step explanation:

The student is asking about calculating the probability of the event that a contestant on a game show lands on "Lose a Turn" all three times when the contestant spins the wheel. Since there are 12 spaces on the wheel and 4 of them are "Lose a Turn", the probability of landing on "Lose a Turn" in one spin is 4/12 or 1/3. The spins are independent events, so to find the probability of the contestant landing on "Lose a Turn" all three times, we multiply the probabilities of each individual event:

Probability of 'Lose a Turn' on all three spins = (1/3) * (1/3) * (1/3)

This equals 1/27. After calculating this value, we should round the answer to four decimal places, which gives us a probability of 0.0370 or 3.70%.