There are 10 people taking part in a raffle.Ann, Bob, Elsa, Hans, Jim, Kira, Lena, Omar, Ravi, and Soo.Suppose that prize winners are randomly selected from the 10 people.Compute the probability of each of the following events.Event A: The first three prize winners are Bob, Kira, and Lena, regardless of order.Event B: Ravi is the first prize winner, Ann is second, and Soo is third.Write your answers as fractions in simplest form.PA = PB =
Question
There are 10 people taking part in a raffle.Ann, Bob, Elsa, Hans, Jim, Kira, Lena, Omar, Ravi, and Soo.Suppose that prize winners are randomly selected from the 10 people.Compute the probability of each of the following events.Event A: The first three prize winners are Bob, Kira, and Lena, regardless of order.Event B: Ravi is the first prize winner, Ann is second, and Soo is third.Write your answers as fractions in simplest form.PA = PB =
Solution
Event A: The first three prize winners are Bob, Kira, and Lena, regardless of order.
The total number of ways to select 3 winners out of 10 people is given by the combination formula C(n, r) = n! / [(n-r)!r!], where n is the total number of people (10), r is the number of winners (3), and "!" denotes factorial.
So, the total number of ways to select 3 winners is C(10, 3) = 10! / [(10-3)!3!] = 720 ways.
Since the order of Bob, Kira, and Lena doesn't matter, there are 3! = 6 ways to arrange these three people.
Therefore, the probability of event A, denoted P(A), is the number of favorable outcomes (6) divided by the total number of outcomes (720).
So, P(A) = 6 / 720 = 1 / 120.
Event B: Ravi is the first prize winner, Ann is second, and Soo is third.
The total number of ways to select 3 winners out of 10 people is still 720.
However, since the order of Ravi, Ann, and Soo does matter in this case, there is only 1 way to arrange these three people.
Therefore, the probability of event B, denoted P(B), is the number of favorable outcomes (1) divided by the total number of outcomes (720).
So, P(B) = 1 / 720.
In conclusion, P(A) = 1 / 120 and P(B) = 1 / 720.
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