Question

A coin is tossed 5 times. Find the probability of getting at least 1 tail.

Answer 1

31/32

Explanation:

If a coin is tossed 5 times, obtaining at least 1 tail means you can either obtain 1,2,3,4, or 5 tails.

`$$\text{P(getting at least one tail in 5 tosses)}$$=1-P(5\text{ heads in 5 tosses)}`

In a coin toss:

`\begin{gathered} P(\text{obtaining head)}=(1)/(2) \\ P(\text{obtaining tails)}=(1)/(2) \end{gathered}`

Therefore:

`P(5\text{ heads in 5 tosses)}=(1)/(2)*(1)/(2)*(1)/(2)*(1)/(2)*(1)/(2)=((1)/(2))^5=(1)/(32)`

This then means that the probability of getting at least 1 tail:

`$$\text{P(getting at least one tail in 5 tosses)}$$=1-(1)/(32)=(31)/(32)`

The probability is 31/32.

Note: You can also solve this problem using the binomial probability formula.