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)0.2
2)0.1
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To calculate the probability, we need to determine the total number of possible outcomes and the number of favorable outcomes for each question.
Question 1: What is the probability that Burt wins?
Total number of possible outcomes: Since there are 5 runners, the total number of possible outcomes is 5! (5 factorial), which is equal to 120.
Favorable outcomes: Burt can win the race in one position. Therefore, the number of favorable outcomes is 1.
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 1/120
Probability ā 0.0083
So, the probability that Burt wins the race is approximately 0.0083 or 0.83%.
Question 2: What is the probability that Burt and Otto occupy the first two places?
Total number of possible outcomes: Since there are 5 runners, the total number of possible outcomes is 5! (5 factorial), which is equal to 120.
Favorable outcomes: Burt and Otto can occupy the first two places in two ways: Burt followed by Otto or Otto followed by Burt. Therefore, the number of favorable outcomes is 2.
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 2/120
Probability ā 0.0167
So, the probability that Burt and Otto occupy the first two places is approximately 0.0167 or 1.67%.
To determine the probability of certain events in this race, we need to identify the total number of possible outcomes and the favorable outcomes that satisfy the conditions of each question.
1. What is the probability that Burt wins?
There are five runners in total, so there are 5! (5 factorial) possible orderings of the runners. Therefore, the total number of possible outcomes is 5! = 120.
The favorable outcome, in this case, is Burt winning. To calculate the probability of Burt winning, we need to find the number of favorable outcomes for Burt winning and then divide it by the total number of possible outcomes.
Since there are five runners, Burt can finish the race in only one position (1st place). Therefore, the number of favorable outcomes for Burt winning is 1.
The probability that Burt wins is favorable outcomes / total possible outcomes = 1/120 = 0.0083 (or approximately 0.01 when rounded to two decimal places).
2. What is the probability that Burt and Otto occupy the first two places?
To determine the probability of Burt and Otto occupying the first two places, we need to find the number of favorable outcomes where Burt and Otto finish the race in the first and second positions, respectively.
Since Burt can only finish in one position (1st place), there are four remaining positions for Otto. Once Burt finishes, there are four possible places for Otto to finish the race.
Therefore, the number of favorable outcomes for Burt and Otto occupying the first two places is 1 * 4 = 4.
The probability that Burt and Otto occupy the first two places is favorable outcomes / total possible outcomes = 4/120 = 0.0333 (or approximately 0.03 when rounded to two decimal places).