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If a coin is flipped three times, what is the probability of getting exactly two

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

Options:

  1. 3/8
  2. 1/2
  3. 1/4
  4. 1/8

Correct Answer: 3/8

Solution: 

The total outcomes are 2^3 = 8. The combinations for exactly 2 heads are HHT, HTH, THH, which gives us 3 favorable outcomes. So, the probability is 3/8.

If a coin is flipped three times, what is the probability of getting exactly two

Practice Questions

Q1
If a coin is flipped three times, what is the probability of getting exactly two heads?
  1. 3/8
  2. 1/2
  3. 1/4
  4. 1/8

Questions & Step-by-Step Solutions

If a coin is flipped three times, what is the probability of getting exactly two heads?
Correct Answer: 3/8
  • Step 1: Understand that when a coin is flipped, it can land on either heads (H) or tails (T).
  • Step 2: Since the coin is flipped three times, we need to find all possible outcomes. Each flip has 2 outcomes, so for 3 flips, the total outcomes are 2^3.
  • Step 3: Calculate 2^3, which equals 8. This means there are 8 possible outcomes when flipping the coin three times.
  • Step 4: List the possible outcomes: HHH, HHT, HTH, HTT, THH, THT, TTH, TTT.
  • Step 5: Identify the outcomes that have exactly 2 heads. These are HHT, HTH, and THH.
  • Step 6: Count the favorable outcomes. There are 3 outcomes with exactly 2 heads.
  • Step 7: To find the probability, divide the number of favorable outcomes (3) by the total outcomes (8).
  • Step 8: The probability of getting exactly 2 heads is 3/8.
  • Probability – Understanding the likelihood of an event occurring, calculated as the ratio of favorable outcomes to total outcomes.
  • Combinatorics – The study of counting, arrangements, and combinations, particularly relevant in determining the number of ways to achieve a specific outcome.
  • Binomial Distribution – A probability distribution that describes the number of successes in a fixed number of independent Bernoulli trials.
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