I’ve answered this before so here’s the complete given for this problem.
Danielle conducts an experiment by tossing a fair coin three times. She records the number of heads out of the three trials. The probabilities are given in the table below (X = number of heads out of three trials).
Given:
x 0 1 2 3
P(x)1/8 3/8 3/8 1/8
n = 3; p = 0.5; q = 0.5; P(x = 0) = nCx p^x
x N(x) P(x) ΣP(x) 1- ΣP(x) x * P(x)
--- ----- --------- --------- --------- ---------
0 1 0.125 0.125 0.875 0
1 3 0.375 0.5 0.5 0.375
2 3 0.375 0.875 0.125 0.75
3 1 0.125 1 0 0.375
0+.375+.75+.375 = 1.5
So, in this problem, the expected number of heads for Danielle's experiment is 1.5.
To add, the measure of the chance that the event will occur as a result of an experiment is called the probability of an event.