Probability Distribution

Question

In a exam, the probability of being awarded a grade A is 0.3.

For a group of ten participants, calculate

(i)the probability of that three achieve grade A

(ii)the probability that at least half achieve grade A.

The probability of being awarded a grade B is also 0.3.

(iii)find the probability that all ten participants achieve either grade A or grade B.

I have done part (i), but getting wrong answer in part (ii) (the answer i got was 0.128..) and also need help in part(iii).

Answer 1

ii) this is a binomial distribution with sample size, n=10 and probability , p=0.3

P(X>=5)=1-P(X<5)=1-P(X<=4)=1-0.8497=0.1503

iii) total probability becomes 0.6 which is bigger than 0.5 so let Y=10-X

so p=1-0.6=0.4

now

P(X=10)=P (10-Y=10) = P(Y=0)= 0.0282