Question

If only 5 percent kids can secure A grade in a paper, find the probability of atmost 2 out of 10 kids getting A grade in that paper?

Answer 1

We use the formula for Binomial Probabilities $P_n(k)=C_n^k p^k q^{n-k}$

p=0,05

q=1-p=1-0,05=0,95

n=10

$k \leqslant 2$

$P_{10}(k\leqslant 2)=P_{10}(k=0)+P_{10}(k=1)+P_{10}(k=2)$  

$P_{10}(k=0)=C_{10}^0 (0.05)^0 (0.95)^ {5-0}=0,5987$

$P_{10}(k=1)=C_{10}^1 (0.05)^1 (0.95)^ {5-1}=0,3151$

$P_{10}(k=2)=C_{10}^2 (0.05)^2 (0.95)^ {5-2}=0,0746$

the probability of at most 2 out of 10 kids getting A grade in that paper is equal to

$P_{10}(k\leqslant 2)=0,5987+0,3151+0,0746=0,9884$