1) 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 first need to determine the possible outcomes and their probabilities.
In any single coin toss, there are two possible outcomes: heads (H) or tails (T). Since the coin is fair, each outcome has an equal probability of occurring, which is 1/2.
Now, let's consider the possible outcomes for 3 coin tosses:
HHH
HHT
HTH
HTT
THH
THT
TTH
TTT
There are 8 possible outcomes in total, each with an equal probability of occurring (1/8).
To find the mean number of heads, we sum up the number of heads in each outcome and divide by the total number of outcomes. Let's assign a value of 1 to heads and 0 to tails:
Mean number of heads = (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.