find the mean number of heads in 3 tosses of a fair coin?
To find the mean number of heads in 3 tosses of a fair coin, we need to consider all possible outcomes and calculate the average.
In a single coin toss, there are two possible outcomes: heads (H) or tails (T), each with a 50% probability.
Let's represent the outcomes of all 3 tosses using H and T:
1. HHH
2. HHT
3. HTH
4. HTT
5. THH
6. THT
7. TTH
8. TTT
Now, let's count the number of heads in each outcome:
1. HHH: 3 heads
2. HHT: 2 heads
3. HTH: 2 heads
4. HTT: 1 head
5. THH: 2 heads
6. THT: 1 head
7. TTH: 1 head
8. TTT: 0 heads
To find the mean number of heads, we sum up the number of heads in each outcome and divide by the total number of possible outcomes (which is 8):
(3 + 2 + 2 + 1 + 2 + 1 + 1 + 0) / 8 = 12 / 8 = 1.5
Therefore, the mean number of heads in 3 tosses of a fair coin is 1.5.