Question

G and H are mutually exclusive events.

Answer 1

Answer:

(1) Correct option is (A)

(2) P (H or G) = 0.80

(3) Correct option is (C)

Step-by-step explanation:

Mutually exclusive events are those events that cannot occur at same time.

If events A and B are mutually exclusive then, P (A and B) = 0.

Given: P (G) = 0.50 and P (H) = 0.30

(1)

The statement is: P (H|G) = 0.40.

The conditional probability of event B given event A is:

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

The probability statement P (H|G) can be written as:

$P(H|G)=\frac{P(H\cap G)}{P(G)}$

But as H and G are mutually exclusive, P (H ∩ G) = 0.

Hence, P (H|G) = 0.

Thus, the provided statement is false because events H and G are mutually exclusive, which makes P(H ∩ G) = 0.

Option (A) is correct.

(2)

The addition rule of probability states that:

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

Compute the value of P (H or G) as follows:

$P(H\cup G)=P(H)+P(G)-P(H\cap G\\=0.30+0.50-0\\=0.80$

Thus, the value of P (H or G) is 0.80.

(3)

Independent events are those events that are not affected by the occurrence of other events.

Events H and G are mutually exclusive events, i.e. occurrence of one affects the occurrence of other.

Thus, events H and G are dependent events.

Option (C) is correct.