Final answer:
To compute the probabilities of different outcomes in flipping an unbiased coin five times, we need to consider the total number of possible outcomes and the number of favorable outcomes for each scenario. The probability of getting exactly three heads is 5/16, the probability of getting at least one tail is 31/32, the probability of getting five heads is 1/32, and the probability of getting an equal number of heads and tails is 5/16.
Step-by-step explanation:
To compute the probabilities of different outcomes in flipping an unbiased coin five times, we need to consider the total number of possible outcomes and the number of favorable outcomes for each scenario.
A. Getting exactly three heads:
- The number of favorable outcomes is the combination of choosing 3 heads out of 5 tosses, which can be calculated as C(5, 3) = 10.
- The total number of possible outcomes is 2^5 = 32 (since each coin toss has 2 possibilities; heads or tails).
- Therefore, the probability of getting exactly three heads is 10/32 = 5/16 = 0.3125.
B. Getting at least one tail:
- The number of favorable outcomes is the complement of getting all heads (which is only one possibility).
- The total number of possible outcomes is still 2^5 = 32.
- Therefore, the probability of getting at least one tail is 1 - 1/32 = 31/32 = 0.96875.
C. Getting five heads:
- The number of favorable outcomes is only one possibility, which is getting all heads.
- The total number of possible outcomes is again 2^5 = 32.
- Therefore, the probability of getting five heads is 1/32 = 0.03125.
D. Getting an equal number of heads and tails:
- The number of favorable outcomes is the combination of choosing 2 heads out of 5 tosses, which can be calculated as C(5, 2) = 10.
- The total number of possible outcomes is 2^5 = 32.
- Therefore, the probability of getting an equal number of heads and tails is 10/32 = 5/16 = 0.3125.