If a basketball player has a shooting percentage of 60% , find the probability that the player will make at least 2 of her next 9 shots?
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To find the probability that the player will make at least 2 of her next 9 shots, we can use the binomial probability formula.
The formula for calculating the probability of x successes in n trials, given a success probability p, is:
P(x) = (nCx) * (p^x) * ((1-p)^(n-x))
Where:
- P(x) is the probability of x successes
- nCx denotes the number of combinations of n items taken x at a time
- p is the probability of success on each trial
- q = 1 - p is the probability of failure on each trial
- x is the number of successes
- n is the number of trials
In this case, the player has a shooting percentage of 60%, which means she has a 0.60 probability of making each shot. Therefore, p = 0.60.
Now, we want to find the probability that the player will make at least 2 of her next 9 shots. This means we need to calculate the probability of getting 2, 3, 4, 5, 6, 7, 8, or 9 successful shots out of the 9 total shots.
Let's calculate it step by step:
P(at least 2 successes) = P(2) + P(3) + P(4) + P(5) + P(6) + P(7) + P(8) + P(9)
P(x) = (nCx) * (p^x) * ((1-p)^(n-x))
Using the formula, we can calculate each individual probability for the different values of x and then add them up to find the overall probability.
P(2) = (9C2) * (0.60^2) * ((1-0.60)^(9-2))
P(3) = (9C3) * (0.60^3) * ((1-0.60)^(9-3))
P(4) = (9C4) * (0.60^4) * ((1-0.60)^(9-4))
P(5) = (9C5) * (0.60^5) * ((1-0.60)^(9-5))
P(6) = (9C6) * (0.60^6) * ((1-0.60)^(9-6))
P(7) = (9C7) * (0.60^7) * ((1-0.60)^(9-7))
P(8) = (9C8) * (0.60^8) * ((1-0.60)^(9-8))
P(9) = (9C9) * (0.60^9) * ((1-0.60)^(9-9))
Finally, sum up all these probabilities to find the overall probability of making at least 2 shots out of the next 9.