Question

If the probability that an event A happens in one trial of an experiment is equal to 0.5 and 4 independent trials are performed then find the probability that the event A happens atleast ones​

Answer 1

Probability that the event A happens at least once is 0.9375.

Step-by-step explanation:

We are given that the probability that an event A happens in one trial of an experiment is equal to 0.5 and 4 independent trials are performed.

The above situation can be represented through binomial distribution;

$P(X=r) = \binom{n}{r}\times p^{r} \times (1-p)^{n-r} ; x = 0,1,2,3,.....$

where, n = number of trials taken = 4

            r = number of success = at least once

           p = probability of success which in our question is probability that

                  an event A happens, i.e; p = 0.5

Let X = Number of times event A happens

So, X ~ Binom(n = 4, p = 0.5)

Now, probability that in 4 independent trials the event A happens at least once is given by = P(X $\geq$ 1)

         P(X $\geq$ 1)  =  1 - P(X = 0)

                        =  $1- \binom{4}{0}\times 0.5^{0} \times (1-0.5)^{4-0}$

                        =  $1-( 1\times 1\times 0.5^{4})$

                        =  1 - 0.0625 = 0.9375

Hence, the probability that the event A happens at least once is 0.9375.