Three fair coins are being tossed.
Let A be the number of heads.
We are asked to find the probability of event A = 2
This means that the probability of getting two heads.
Recall that the probability of an event is given by
[tex]P(A=2)=\frac{\text{outcomes of interest}}{total\text{ outcomes}}[/tex]The outcomes of interest are the number of outcomes in which we can get 2 heads.
Let us first find all the possible outcomes when we toss three fair coins.
Sample space = {HHH, HHT, HTH, THH, TTH, THT, HTT, TTT}
As you can see, there are 3 outcomes in which we can get 2 heads.
The total number of outcomes is 8.
So, the probability is
[tex]P(A=2)=\frac{\text{outcomes of interest}}{total\text{ outcomes}}=\frac{3}{8}=0.375[/tex]Therefore, the probability of event A = 2 (getting 2 heads) is 0.375
