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The probability that Laura wins a tennis match against Jennifer is 2/3 . What is the probability that Laura wins exactly three of the next four matches she plays against Jennifer?

1) 32/81
2) 8/81
3) 108/256
4) 27/256

User Omurbek
by
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1 Answer

1 vote

Final answer:

To find the probability that Laura wins exactly three out of the next four matches against Jennifer, we can use the binomial probability formula.

Step-by-step explanation:

To find the probability that Laura wins exactly three out of the next four matches against Jennifer, we can use the binomial probability formula. The formula is:

P(X=k) = C(n, k) * p^k * (1-p)^(n-k)

Where:

  • P(X=k) is the probability of getting 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 a success in a single trial
  • n is the total number of trials
  • k is the number of successes

In this case, Laura winning a match is a success and Jennifer winning a match is a failure. We want to find the probability of exactly 3 successes out of 4 trials, so n = 4 and k = 3. The probability of Laura winning a match is p = 2/3.

Therefore, plugging these values into the formula, we have:

P(X=3) = C(4, 3) * (2/3)^3 * (1-(2/3))^(4-3)

Simplifying this equation gives us:

P(X=3) = 4 * (2/3)^3 * (1/3)^1

P(X=3) = 4 * 8/27 * 1/3

P(X=3) = 32/81

So the probability that Laura wins exactly three of the next four matches she plays against Jennifer is 32/81.

User AlBeebe
by
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