find the mean number of heads in 3 tosses of a fair coin?
HTT
HHt
HHH
TTT
mean= total/ways=6/4=1.5
To find the mean number of heads in 3 tosses of a fair coin, we need to calculate the expected value. The expected value, or mean, is obtained by multiplying the value of each outcome by its probability and summing them up.
For a fair coin, there are two possible outcomes for each toss: heads (H) or tails (T). Both outcomes have an equal probability of 0.5 (since the coin is fair).
To calculate the mean, we need to consider all possible outcomes. In this case, we have:
1. HHH (3 heads) - Probability: (0.5)^3 = 0.125
2. HHT (2 heads, 1 tail) - Probability: (0.5)^3 = 0.125
3. HTH (2 heads, 1 tail) - Probability: (0.5)^3 = 0.125
4. THH (2 heads, 1 tail) - Probability: (0.5)^3 = 0.125
5. HTT (1 head, 2 tails) - Probability: (0.5)^3 = 0.125
6. THT (1 head, 2 tails) - Probability: (0.5)^3 = 0.125
7. TTH (1 head, 2 tails) - Probability: (0.5)^3 = 0.125
8. TTT (0 heads) - Probability: (0.5)^3 = 0.125
Now, we calculate the mean by multiplying each outcome by its probability and summing them up:
Mean = (3 * 0.125) + (2 * 0.125 * 3) + (1 * 0.125 * 3) + (0 * 0.125) = 1.5
Therefore, the mean number of heads in 3 tosses of a fair coin is 1.5.