Question

3.2 Independent and Mutually Exclusive Events 

40. E and Fare mutually exclusive events. P(E) = 0.4; P(F) = 0.5. Find P(E|F)

41. J and K are independent events. P(J|K) = 0.3. Find P(J) 

42. U and V are mutually exclusive events. P(U) = 0.26: P(V) = 0.37. Find:

a. P(U AND V) =

a. P(U|V) =

a. P(U OR V) =

43. Q and Rare independent events P(Q) = 0.4 and P(Q AND R) = 0.1. Find P(R)

Answer 1

40

\(P(E \mid F)=\frac{P(E \cap F)}{P(F)}=\frac{P(\phi)}{P(F)}=0\) [Since, \(\mathrm{E}\) and \(\mathrm{F}\) are mutually exclusive]

41

Since \(J\) and \(K\) are independent variables,

\(P(J \mid K)=\frac{P(J \cap K)}{P(K)}=\frac{P(J) \cdot P(K)}{P(K)}=P(J)=0.3\)

42 a.

\(P(U A N D V)=P(U \cap V)=P(\phi)=0\)

\(42 \mathrm{~b} .\)

\(P(U \mid V)=P(U \cap V) / P(V)=P(\phi) / 0.37=0\)

42c.

\(P(U O R V)=P(U \cup V)=P(U)+P(V)=0.26+0.37=0.63\)

\(\underline{43}\)

$$ \begin{aligned} &P(Q A N D R)=P(Q \cap R)=P(Q) \cdot P(R)=0.1 \\ &\therefore P(R)=0.1 / P(Q)=0.1 / 0.4=0.25 \end{aligned} $$