G and H are mutually exclusive events. P(G)=0.5P(H)=0.3

a. Explain why the following statement MUST be false: P(H|G)=0.4.

b. Find P(HORG).

c. Are G and H independent or dependent events? Explain in a complete sentence

Short Answer

Expert verified

(a) PGandH=0as G and H are mutually exclusive events, hence the statement PH|G=0.4must be false.

(b) localid="1648908239487" PHORG=0.8.

(c) G and H are dependent events.

Step by step solution

01

Given information (part a)

G and H are mutually exclusive events.PG=0.5andPH=0.3

02

Explanation (part a)

Given that PG=0.5andPH=0.3

We need to calculate PH|G

PGandH=PG|H×PHPG|H=PGandHPH

Also, G and H are mutually exclusive events,

PGandH=0

Thus, we have

localid="1649420858160" PG|H=00.3PG|H=0

03

Given information (part b)

G and H are mutually events.PG=0.5andPH=0.3

04

Explanation (part b)

PG=0.5andPH=0.3

Also, GandH are mutually exclusive events,

PGandH=0

Thus, PHorGis calculated as

PHorG=PH+PG-PHandGPHorG=0.3+0.5-0PHorG=0.8

05

Given information (part c)

G and H are mutually exclusive events.PG=0.5andPH=0.3

06

Explanation (part c)

Given that G and H are mutually exclusive events,

PGandH=0

The information that one event has occurred completely determines the probability of the other event, which is zero in this case. Thus, both events cannot occur at the same time, and therefore the events are dependent on each other.

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