Question

Three fair coins are tossed, what is the probability that exactly two heads are obtained?

Answer 1

On each coin, the probability of heads and the probability of tails are both 1/2.

There are 3 ways to toss 3 coins such that exactly 2 heads are obtained: HHT, HTH, THH.

So the desired probability is

3(1/2)(1/2)(1/2) = 3/8

Answer 2

Probability is
`\sf (3 )/( 8)` or 37.5 %

Explanation:

To find the probability of exactly two heads in three fair coin tosses, we need to consider all the possible outcomes and count the favorable outcomes where we get exactly two heads.

Total possible outcomes when tossing three fair coins:

`\sf 2^3 = 8` Possible outcomes.

(each coin can have two outcomes: heads or tails)

The favorable outcomes to get exactly two heads:

• HHT (Head, Head, Tail)
• HTH (Head, Tail, Head)
• THH (Tail, Head, Head)

So, there are 3 favorable outcomes.

Now,

`\sf Probability =\frac{ \textsf{Number of favorable outcomes}}{\textsf{ Total number of possible outcomes}}`

Substituting value

`\sf Probability = (3 )/( 8)`

In Percentage

`\sf (3 )/( 8)*100`

= 37.5 %
Therefore, the probability of exactly two heads in three fair coin tosses is
`\sf (3 )/( 8)` or 37.5 %