What Are The Odds Of Getting 3 Heads In 3 Flips?
Exactly Three Heads In Five Flips | Probability And Statistics | Khan Academy
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What Are The Odds Of 3 Heads In 4 Flips?
What is the likelihood of obtaining three heads in a sequence of four coin flips? To calculate this probability, we need to consider the different combinations that result in three heads. These combinations are HTHH, HHHT, and THHH. To find the odds of getting exactly three heads in four flips of a fair coin, we divide the number of favorable outcomes (3) by the total possible outcomes (16). This yields a probability of 3/16, which is equivalent to 0.1875 or 18.75%. So, the chance of obtaining three heads in four coin flips is 18.75%.
What Are The Probabilities Of 3 Coin Flips?
Let’s provide a clearer explanation of the probabilities of getting specific outcomes in three coin flips:
When we flip a fair coin three times (which means each flip has an equal chance of landing heads, H, or tails, T), we want to determine the probability of a particular sequence, like HTH (Heads, Tails, Heads). Since each coin flip is independent, we can calculate this probability by multiplying the individual probabilities of each outcome.
In this case, the probability of getting Heads (H), p(H), and the probability of getting Tails (T), p(T), are both equal to 1/2 because the coin is fair, meaning there’s an equal chance of getting either outcome.
So, to find the probability of getting HTH, we multiply these probabilities: p(H) × p(T) × p(H) = (1/2) × (1/2) × (1/2) = 1/8. This means there’s a 1/8 chance of getting the sequence HTH when flipping a fair coin three times, which is equivalent to 12.5%.
Example 2: [You can similarly calculate the probabilities for other sequences by multiplying the individual probabilities of each outcome in the sequence.]
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If you flip a coin 3 times, what are the odds that the coin will be heads all three times? Explanation: If you flip a coin, the chances of you getting heads is 1/2. This is true every time you flip the coin so if you flip it 3 times, the chances of you getting heads every time is 1/2 * 1/2 * 1/2, or 1/8.There are 3 combinations that have 3 heads: HTHH, HHHT, and THHH. So the odds of getting exactly 3 heads in four flips of a fair coin is 3/16 or 0.1875, or 18.75%.If you toss a coin 3 times, the probability of at least 2 heads is 50%, while that of exactly 2 heads is 37.5%. Here’s the sample space of 3 flips: {HHH, THH, HTH, HHT, HTT, THT, TTH, TTT}. There are 8 possible outcomes. Three contain exactly two heads, so P(exactly two heads) = 3/8=37.5%.
- ( H , T , H ) Since the flips are independent this is.
- p ( H , T , H ) = p H p T p H. Since the coin is fair we have.
- p H = p T = 1 2. so.
- p H p T p H = 1 2 × 1 2 × 1 2 = 1 8. So the answer is 1/8, or 12.5%. Example 2.
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