Question

Find the indicated probability. Round your answer to 6 decimal places when necessary.Three "fair" coins are tossed. Let A be number of heads. What is the probability of event A = 2?

Answer 1

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

`P(A=2)=\frac{\text{outcomes of interest}}{total\text{ outcomes}}`

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

`P(A=2)=\frac{\text{outcomes of interest}}{total\text{ outcomes}}=(3)/(8)=0.375`

Therefore, the probability of event A = 2 (getting 2 heads) is 0.375