Question

U and V are mutually exclusive events. P(U) = 0.27; P(V) = 0.56. Find:

Answer 1

$\because$ U and V are mutually exclusive events.

Answer 2

Answer:

(a) P (U and V) = 0.

(b) P (U|V) = 0.

(c) P (U or V) = 0.83.

Step-by-step explanation:

Mutually exclusive events are those events that cannot occur at the same time. That is, if events A and B are mutually exclusive then,

                                         $P (A\cap B) = 0$

Given:

Events U and V are mutually exclusive.

P (U) = 0.27 and P (V) = 0.56

(a)

As events U and V are mutually exclusive, the probability of their intersection will be 0.

That is,

$P(U\ and\ V) = P (U\cap V) = 0$

Thus, the value of P (U and V) is 0.

(b)

The conditional probability of event B given A is:

$P(B|A) =\frac{P(A\cap B)}{P(B)}$

Compute the value of P (U|V) as follows:

$P(U|V) =\frac{P(U\cap V)}{P(V)}\\=\frac{0}{0.56}\\ =0$

Thus, the value of P (U|V) is 0.

(c)

The probability of the union of two events, say A and B, is

$P(A\ or\ B)=P(A\cup B)=P(A)+P(B)-P(A\cap B)$

Compute the value of P (U or V) as follows:

$P(U\ or\ V)=P(U\cup V)\\=P(U)+P(V)-P(U\cap V)\\=0.27+0.56-0\\=0.83$

Thus, the value of P (U or V) is 0.83.