Fred, Burt, Conrad, Otto, and Hugh run a race. All the runners can be taken to have the same level of ability, so it may be assumed that all of the possible orderings of the five runners are equally likely. Express your answers to the questions to two decimals.
What is the probability that Burt wins? ]
What is the probability that Burt and Otto occupy the first two places?
1/5
1/20
To find the probability that Burt wins the race, we need to calculate the number of favorable outcomes (Burt finishing first) and the total number of possible outcomes.
The total number of possible outcomes is given by the number of permutations of the five runners, which is 5! = 120. This means that there are 120 different arrangements of the runners.
The number of favorable outcomes is just 1, as there is only one way for Burt to finish first.
Therefore, the probability that Burt wins the race is 1/120, which can be expressed as 0.0083 (rounded to two decimal places).
To find the probability that Burt and Otto occupy the first two places, we need to calculate the number of favorable outcomes (Burt and Otto finishing first and second) and the total number of possible outcomes.
The total number of possible outcomes remains the same, 120.
To calculate the number of favorable outcomes, we need to consider that both Burt and Otto must finish in the first two places. There are 2 ways this can happen: Burt first and Otto second, or Otto first and Burt second.
Therefore, the number of favorable outcomes is 2.
The probability that Burt and Otto occupy the first two places is 2/120, which can be expressed as 0.0167 (rounded to two decimal places).