In a game hold by class, about 3 people out of 10 will win a price. If 30 people join the game, what is the probability that 10 people won the price? (the result is omitted to 2 decimals)
Question
In a game hold by class, about 3 people out of 10 will win a price. If 30 people join the game, what is the probability that 10 people won the price? (the result is omitted to 2 decimals)
Solution
This is a binomial probability problem. The formula for binomial probability is:
P(X=k) = C(n, k) * (p^k) * ((1-p)^(n-k))
where:
- P(X=k) is the probability of k successes in n trials
- C(n, k) is the number of combinations of n items taken k at a time
- p is the probability of success on a single trial
- n is the number of trials
- k is the number of successes
In this case:
- n = 30 (the number of people who join the game)
- k = 10 (the number of people we want to win the prize)
- p = 3/10 = 0.3 (the probability of winning a prize)
Substituting these values into the formula, we get:
P(X=10) = C(30, 10) * (0.3^10) * ((1-0.3)^(30-10))
Calculating the above expression gives a probability of approximately 0.27 when rounded to two decimal places.
So, the probability that 10 people win the prize is 0.27.
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