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Chapter 7: Problem 2

Find the probability of the given event. The coin lands heads exactly once.

Short Answer

Expert verified
The probability of the coin landing heads exactly once in one flip is \(\frac{1}{2}\), or 50%.

Step by step solution

01

Identify the given information

In this problem, we are given: n = 1 (since we are concerned about only one coin flip), k = 1 (we want the coin to land heads exactly once), and p = 1/2 (the probability of getting heads in each flip).
02

Calculate C(n, k)

Next, we need to calculate the number of combinations of n objects taken k at a time (C(n, k)): C(n, k) = n! / (k! * (n-k)!) In this case: C(1, 1) = 1! / (1! * (1-1)!) = 1 / (1 * 1) = 1
03

Apply the binomial probability formula

Now that we have C(n, k), we can use the binomial probability formula: P(X = k) = C(n, k) * p^k * (1 - p)^(n-k) Substitute the values: P(X = 1) = C(1, 1) * (1/2)^1 * (1 - 1/2)^(1-1) P(X = 1) = 1 * (1/2) * (1/2)^0 P(X = 1) = 1 * (1/2) * 1 P(X = 1) = 1/2
04

Interpret the result

The probability of the coin landing heads exactly once in one flip is 1/2, or 50%.

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Most popular questions from this chapter

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