Question

In a race of 10 flips, if tails are flipped first, what is the probability that there are more heads than tails in the 10 flips?

a) 0.25
b) 0.50
c) 0.75
d) 1.00

Answer 1

The probability of getting more heads than tails in a race of 10 flips, given that tails are flipped first, can be calculated to be approximately 0.6113.

Step-by-step explanation:

The probability of getting more heads than tails in a race of 10 flips, given that tails are flipped first, can be calculated by considering the number of possible outcomes. Let's break it down step by step:

1. First, we need to find the number of ways to arrange the 10 flips. This can be calculated using the concept of combinations. The number of ways to arrange 10 flips is equal to 2^10, as each flip can have 2 possible outcomes (heads or tails).
2. Next, we need to determine the number of outcomes where there are more heads than tails. This can be calculated by adding up the number of outcomes with 6, 7, 8, 9, or 10 heads.
3. The probability of getting more heads than tails is then calculated by dividing the number of outcomes with more heads than tails by the total number of possible outcomes.
4. In this case, there are 252 outcomes with 6 heads, 210 outcomes with 7 heads, 120 outcomes with 8 heads, 45 outcomes with 9 heads, and 10 outcomes with 10 heads. Adding all these up gives us a total of 627 outcomes with more heads than tails.
5. The total number of possible outcomes is 2^10 = 1024. So, the probability of getting more heads than tails is 627/1024 ≈ 0.6123, or approximately 0.61.

Therefore, the correct answer is not provided in the options given. The probability is approximately 0.6113, which is not represented by any of the options.