Question

The probabilities that student will receive $A,B,C$ or $D$ grade are $0.40,0.35,0.15$ and $0.10$ respectively. Find the probability that a student will recive
i) not an A grade
ii) B or C grade
iii) at most C grade

Answer 1

let the probability that student receive $A$

grade be $P\left(A\right)$

$P\left(A\right)=0.40$

sim. $P\left(B\right)=0.35$

$P\left(C\right)=0.15$ and $P\left(D\right)=0.10$

(i) not an $A$ grade

$P$ (not on $A$ grade)$=1-P\left(A\right)$

$=1-0.40$

$=0.60$

(ii) $B$ or $C$ grade

$P$($B$ or $C$ grade) $=P\left(B\right)+P\left(C\right)$

$=0.35+0.15$

$=0.50$

(iii) $P$ (at most $C$ grade) $=P\left(C\right)+P\left(D\right)$

$=0.15+0.10$

$=0.25$