Question

A single coin is tossed $5$ times. What is the probability of getting at least one head?
A. $\dfrac{{27}}{{32}}$
B. $\dfrac{3}{{32}}$
C. $\dfrac{1}{{32}}$
D. $\dfrac{{31}}{{32}}$

Answer 1

Hint : As we know that probability is the prediction of a particular outcome of a random event. It is a set of all the possible outcomes for a random experiment. We can calculate the question with the formula of probability i.e. Probability $= \dfrac{{No.\,\,of\,favourable\,\,outcomes}}{{Total\,\,number\,\,of\,\,outcomes}}$ . Let us assume a coin to be fair and $2 -$ sides. When we flip the coin five times, it has ${2^5} = 32$ outcomes. So we have the total number of outcomes $= 32$ .

Complete step-by-step answer :
We have the total number of cards $= 32$ .
We can show the outcomes using the Sample space then $S = (H,H,H,H,H),(H,H,H,H,T),...,(T,H,H)$ .
So we can see that the probability of all tails in $5$ throws is $\dfrac{1}{{32}}$ .
We can say that the probability of getting at least one head $= 1 -$ probability of one head.
So the required probability by putting value is $1 - \dfrac{1}{{32}}$ .
On solving it gives us $\dfrac{{32 - 1}}{{32}} = \dfrac{{31}}{{32}}$
Hence the correct option is (d) $\dfrac{{31}}{{32}}$ .
So, the correct answer is “Option D”.

Note : We should be careful that we have to find the probability of at- least one head , so we have to subtract it. If we see the complement of at least one tail means $0$ tails or $5$ heads, then we must surely see $1$ outcome i.e. all heads. Then we can say that it must follow at least one tail that has $31$ outcomes i.e. $32 - 1 = 31$ .