Question

Given two independent events $A$ and $B$ such that $P(A)=0.3,P(B)=0.6.$ Find:
(A)$P(A\, and\, B)$
(B)$P(A\, and\, not\, B)$
(C)$P(A or B)$
(D)$P(neither\, A\, nor\, B)$

Answer 1

It is given that P(A)=0.3,$$P(B)=0.6
$A$ and $B$ are independent events.

---

(i)$P(A\, and\, B)=P(A).P(B)$
$\implies P(A\cap B)=0.3\times 0.6$
$=0.18$

---

(ii)$P$($A$ and not $B$)$=P(A∩B')$
$=P(A)–P(A∩B)$
$=0.3–0.18$
$=0.12$

---

(iii)$P$($A$ or $B$)
$=P(A)+P(B)–P$($A$ and $B$)
$=0.3+0.6–0.18$
$=0.9–0.18$
$=0.72$

---

(iv)$P$(neither $A$ nor $B$)=$P(A'\cap B')$
$=1–P(A∪B)$
$=1–0.72$
$=0.28$