Here’s a breakdown of the probability of a fair coin toss occurring three times:
- Each toss is an independent event: This means the outcome of one toss doesn’t affect the outcome of the others.
- Two possible outcomes per toss: Each flip can result in either heads (H) or tails (T).
- Probability of heads or tails is 1/2 (0.5 or 50%) for each toss: Assuming a fair coin.
Since there are 2 possible outcomes for each of the 3 tosses, the total number of possible outcomes is 2 2 2 = 2 3 2 cubed 2 3 = 8.
These outcomes can be listed as:
- HHH
- HHT
- HTH
- HTT
- THH
- THT
- TTH
- TTT
- Probability of all three being heads (HHH): Since each toss is independent, you multiply the probabilities together: (1/2) (1/2) (1/2) = 1/8 or 12.5%.
- Probability of all three being tails (TTT): Similarly, the probability is 1/8 or 12.5%.
- Probability of specific sequences (e.g., HTH): The probability of any specific sequence of three tosses is also 1/8 or 12.5%.
- Probability of getting exactly two heads (and one tail): Count the number of outcomes with two heads (HHT, HTH, THH), there are 3 such outcomes. Divide this by the total number of outcomes: 3/8 or 37.5%.
- Probability of getting at least one head: The easiest way to calculate this is to consider the complementary event (not getting at least one head), which is getting all tails. Since the probability of all tails is 1/8, the probability of at least one head is $1 – (1/8) = 7/8.
The probability of individual outcomes in a series of fair coin tosses is found by multiplying the probabilities of each independent toss together. Different events or combinations of outcomes will have varying probabilities depending on the number of favorable outcomes compared to the total possible outcomes.
How many possible outcomes are there if you flip a coin 3 times?
There are eight possible outcomes of tossing the coin three times, if we keep track of what happened on each toss separately. In three of those eight outcomes (the outcomes labeled 2, 3, and 5), there are exactly two heads. This way of counting becomes overwhelming very quickly as the number of tosses increases.
What is the probability of flipping a coin heads 3 times in a row?
Answer: If a coin is tossed three times, the likelihood of obtaining three heads in a row is 1/8. Let’s look into the possible outcomes.
What is the probability of rolling a dice 3 times?
Great question! With 3 dice there are 6^3 = 216 permutations possible, all equally likely. As you say, the probability of getting 3 unique rolls is 1*5/6*4/6 = 20/36. So, there are 216 * 20/36 = 120 permutations that have three unique results.
What is the probability of flipping a coin 3 times and it landing on tails all 3 times?
Answer: The probability of flipping a coin three times and getting 3 tails is 1/8.