If you flip a fair coin three times, what is the probability of getting exactly

₹0.0

Question: If you flip a fair coin three times, what is the probability of getting exactly two heads?

Options:

Correct Answer: 3/8

Solution:

The probability of getting exactly 2 heads in 3 flips = C(3,2) * (1/2)^2 * (1/2)^1 = 3/8.

If you flip a fair coin three times, what is the probability of getting exactly two heads?

If you flip a fair coin three times, what is the probability of getting exactly two heads?

Step 1: Understand that a fair coin has two sides: heads (H) and tails (T).
Step 2: When you flip the coin three times, you can get different combinations of heads and tails.
Step 3: We want to find the probability of getting exactly 2 heads in those 3 flips.
Step 4: Use the combination formula C(n, k) to find how many ways we can choose 2 heads from 3 flips. Here, n = 3 (total flips) and k = 2 (number of heads).
Step 5: Calculate C(3, 2), which is equal to 3. This means there are 3 different ways to get 2 heads in 3 flips.
Step 6: Each flip of the coin has a probability of 1/2 for heads and 1/2 for tails.
Step 7: Since we want 2 heads and 1 tail, we calculate the probability as (1/2)^2 for the heads and (1/2)^1 for the tail.
Step 8: Multiply the number of combinations (3) by the probability of getting 2 heads and 1 tail: 3 * (1/2)^2 * (1/2)^1.
Step 9: Simplify the calculation: 3 * (1/4) * (1/2) = 3/8.
Step 10: Therefore, the probability of getting exactly 2 heads when flipping a coin 3 times is 3/8.

Binomial Probability – The question tests understanding of binomial probability, specifically calculating the probability of a certain number of successes (heads) in a fixed number of trials (coin flips).
Combinatorics – It involves using combinations to determine the number of ways to achieve the desired outcome (2 heads in 3 flips).
Probability Basics – The question requires knowledge of basic probability principles, including the probability of independent events.