Question

a fair coin is tossed repeatedly. find the probability that a fair coin is flipped a multiple of three times before coming up heads.

Answer 1

The probability is 1/4.

Step-by-step explanation:

To find the probability that a fair coin is flipped a multiple of three times before coming up heads, we need to consider the possible outcomes of the coin flips.

A fair coin has two possible outcomes: heads (H) or tails (T), each with a probability of 0.5.

If the coin is flipped once, there are two possible outcomes: H or T.

If the coin is flipped twice, there are four possible outcomes: HH, HT, TH, or TT.

If the coin is flipped three times, there are eight possible outcomes: HHH, HHT, HTH, HTT, THH, THT, TTH, or TTT.

We can see that there are two outcomes (HHT and THH) where the coin is flipped a multiple of three times before coming up heads.

Therefore, the probability is 2/8 or 1/4.

Answer 2

The probability that a fair coin is flipped a multiple of three times before coming up heads is 0.5703.

Step-by-step explanation:

To find the probability that a fair coin is flipped a multiple of three times before coming up heads, we can divide the problem into three cases:

1. The coin is flipped 0 times before coming up heads.
2. The coin is flipped 3 times before coming up heads.
3. The coin is flipped 6 times before coming up heads.

In each case, the probability of getting heads on the next flip is 0.5, and the probability of getting tails is also 0.5.

Therefore, the probability of flipping a multiple of three times before coming up heads is the sum of the probabilities of these three cases:

P(multiple of three times before heads) = P(0 times before heads) + P(3 times before heads) + P(6 times before heads) = (0.5)^1 + (0.5)^4 + (0.5)^7 = 0.5 + 0.0625 + 0.0078 = 0.5703