Question

He probability that a man can hit a target is 3/4. he tries 5 times. the probability that he will hit the target at least three times is:

Answer 1

the method of doing these type of questions is by binomial probability.

Answer 2

Answer:

0.89

Step-by-step explanation:

Probability of hitting target = 3/4

probability of not hitting target = $1-\frac{3}{4}=\frac{1}[4}$

Now we are Supposed to find the probability that he will hit the target at least three times(i.e. ≥3)  out of 5 times

So we will use binomial formula :

$P(X)=^nC_rp^rq^{n-r}$

where p is probability of success

q is probability of failure

n is no. of trials

So, the probability that he will hit the target at least three times

$P(X)=^5C_3 \times (\frac{3]{4})^3 (\frac{1}{4})^{5-3}+5C_4\times(\frac{3]{4})^4 (\frac{1}{4})^{5-4}+5C_5\times(\frac{3]{4})^5 (\frac{1}{4})^{5-5}$

$P(X)=^5C_3\times(\frac{3]{4})^3 (\frac{1}{4})^{2}+5C_4\times(\frac{3]{4})^4 (\frac{1}{4})^{1}+5C_5\times(\frac{3]{4})^5 (\frac{1}{4})^{0}$

$P(X)= 0.263671875+0.3955078125+0.2373046875$

$P(X)= 0.89$

Hence the probability that he will hit the target at least three times is 0.89