Question

A fair coin is tossed five times. Use the binomial probability formula to calculate the probability of at least four heads.

Answer 1

To calculate the probability of getting at least four heads when tossing a fair coin five times, you can use the binomial probability formula. The probability of getting at least four heads is 0.1875.

Step-by-step explanation:

To calculate the probability of getting at least four heads when tossing a fair coin five times, we can use the binomial probability formula:

P(X ≥ k) = 1 - P(X < k)

Where X represents the number of heads, k represents the desired number of heads, and P(X < k) is the cumulative probability of getting less than k heads.

In this case, we want to find the probability of at least four heads, so k = ≥ 4. Using the binomial probability formula:

P(X ≥ 4) = 1 - P(X < 4)

The cumulative probability of getting less than four heads can be calculated by summing the probabilities of getting 0, 1, 2, or 3 heads.

Let's calculate this:

1. P(X = 0) = (5 choose 0) * (0.5)^0 * (0.5)^5 = 1 * 1 * 0.03125 = 0.03125
2. P(X = 1) = (5 choose 1) * (0.5)^1 * (0.5)^4 = 5 * 0.5 * 0.0625 = 0.15625
3. P(X = 2) = (5 choose 2) * (0.5)^2 * (0.5)^3 = 10 * 0.25 * 0.125 = 0.3125
4. P(X = 3) = (5 choose 3) * (0.5)^3 * (0.5)^2 = 10 * 0.125 * 0.25 = 0.3125

Adding up these probabilities:

P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.03125 + 0.15625 + 0.3125 + 0.3125 = 0.8125

Using the formula, we can find the probability of getting at least four heads:

P(X ≥ 4) = 1 - P(X < 4) = 1 - 0.8125 = 0.1875