Question

A fair coin is tossed three times in succession. the set of equally likely outcomes is startset hhh comma hht comma hth comma thh comma htt comma tht comma tth comma ttt endset. find the probability of getting exactly one head.

Answer 1

Solution:

As Given a coin is tossed thrice.

Total possible outcome = {HHH, TTT,HHT,HTH,THH,TTH,THT,HTT}=8

Total Favorable outcome = Exactly one Head = {TTH, THT,HTT} = 3

Probability of getting exactly one head = $\frac{\text{Total favorable outcome}}{\text{Total Possible Outcome}}$

          = $\frac{3}{8}$

Answer 2

The probability helps us to know the chances of an event occurring. The probability of getting exactly one head in the three tosses is 0.375.

What is Probability?

The probability helps us to know the chances of an event occurring.

$\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}$

The possible outcomes of three coin tosses are:

1. HHH
2. HHT
3. HTH
4. HTT
5. THH
6. THT
7. TTH
8. TTT

Now, the number of outcomes that has exactly one head is HTT, TTH and THT,  therefore, 3, while the total number of outcomes is 8. Thus, the probability can be written as,

$\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}$

$\rm Probability=\dfrac{\text{Number of outcomes that have only one head}}{\text{Total Number of Heads}}\\\\\rm Probability=\dfrac{3}{8} = 0.375$

Hence, the probability of getting exactly one head in the three tosses is 0.375.

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