A fair coin is tossed 3 times in a row. If X is the number of heads counted, what is the mean of the probability distribution of X?
A) 1.0
B) 1.5
C) 2.0
D) 2.5
E) 3.0
To determine the mean of the probability distribution of X, we need to calculate the expected value. In this case, X represents the number of heads obtained when a fair coin is tossed 3 times.
The formula for the expected value is:
E(X) = Σ(x * P(x))
Where x represents the possible values of X, and P(x) represents the probability of obtaining each value.
To solve this, let's consider all possible values of X:
When tossing a coin 3 times, the possible values for X are 0, 1, 2, and 3.
Now, let's calculate the probability of obtaining each value:
P(X = 0) = P(TTT) = (1/2) * (1/2) * (1/2) = 1/8
P(X = 1) = P(HTT, THT, TTH) = 3 * ((1/2) * (1/2) * (1/2)) = 3/8
P(X = 2) = P(HHT, HTH, THH) = 3 * ((1/2) * (1/2) * (1/2)) = 3/8
P(X = 3) = P(HHH) = (1/2) * (1/2) * (1/2) = 1/8
Now, let's calculate the expected value using the formula mentioned above:
E(X) = (0 * 1/8) + (1 * 3/8) + (2 * 3/8) + (3 * 1/8)
= 0 + 3/8 + 6/8 + 3/8
= 12/8
= 3/2
= 1.5
Therefore, the mean of the probability distribution of X is 1.5.
The correct answer is B) 1.5.