G and H are mutually exclusive events.

• P(G) = 0.5
• P(H) = 0.3

1.) Explain why the following statement MUST be false: P(H | G) = 0.4. (Select a letter for your answer)

(A.)The events are mutually exclusive, which makes P(H AND G) = 0; therefore, P(H | G) = 0.

(B.)The statement is false because P(H | G) = P(H)/P(G)= 0.6

(C.) The events are mutually exclusive, which means they can be added together, and the sum is not 0.4.

(D.)To find conditional probability, divide P(G AND H) by P(H), which gives 0.5.

2.) Find P(H OR G).

3.) Are G and H independent or dependent events? Explain. (Select a letter for your answer)

(A.) G and H are dependent events because P(G OR H) ≠ 1.

(B.) G and H are independent events because they are mutually exclusive.

(C.) G and H are dependent events because they are mutually exclusive.T

(D.) There is not enough information to determine if G and H are independent or dependent events

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warylucknow warylucknow · Answer 1 · 2020-02-07T10:45:43+01:00

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:

[tex]P(B|A)=\frac{P(A\cap B)}{P(A)}[/tex]

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

[tex]P(H|G)=\frac{P(H\cap G)}{P(G)}[/tex]

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:

[tex]P(A\cup B)=P(A)+P(B)-P(A\cap B)[/tex]

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

[tex]P(H\cup G)=P(H)+P(G)-P(H\cap G\\=0.30+0.50-0\\=0.80[/tex]

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.