Question

Heather has a coin that has a 60% chance of showing heads each time it is flipped. She is going to flip the coin 5 times. Let X represent the number of heads she gets. What is the probability that she gets exactly 3 heads?

a) 0.032

b) 0.138

c) 0.432

d) 0.576

Answer 1

To find the probability of getting exactly 3 heads when flipping a coin 5 times, we can use the binomial probability formula. Plugging in the values, we get a probability of 0.3456, which is closest to option (c) 0.432.

Step-by-step explanation:

To find the probability of getting exactly 3 heads when flipping a coin 5 times, we need to use the binomial probability formula.

The formula is P(X=k) = (nCk) * p^k * q^(n-k), where n is the number of trials, k is the number of successes, p is the probability of success, and q is the probability of failure.

In this case, n = 5, k = 3, p = 0.6 (the probability of heads), and q = 0.4 (the probability of tails).

Plugging in the values, we get P(X=3) = (5C3) * 0.6^3 * 0.4^2 = 10 * 0.216 * 0.16 = 0.3456.

So, the probability that Heather gets exactly 3 heads is 0.3456, which is closest to option (c) 0.432.