Question

Assuming there is a 0.5 probability that a coin will land on heads, what is the probability of getting heads, then heads, then tails, and then heads again?

a) 0.0625
b) 0.125
c) 0.25
d) 0.5

Answer 1

The probability of getting heads, then heads, then tails, and then heads again in a coin toss is calculated by multiplying the individual probabilities of each event, which is 0.5 for each toss. Therefore, the total probability is 0.5^4, which equals 0.0625.

Step-by-step explanation:

The probability of a series of coin toss outcomes. When considering independent events, where the outcome of one event does not influence the outcome of another, we multiply the probabilities of each event occurring. In this case, the probability of getting heads, then heads, then tails, and then heads again is calculated as follows:

• Probability of first coin being heads: 0.5
• Probability of second coin being heads: 0.5
• Probability of third coin being tails: 0.5
• Probability of fourth coin being heads: 0.5

Multiplying these probabilities together: 0.5 (for the first head) × 0.5 (for the second head) × 0.5 (for the tail) × 0.5 (for the third head) equals 0.5^4 which is 0.0625.

Therefore, the probability of getting heads, then heads, then tails, and then heads again is 0.0625, which corresponds to option (a).