Question

question 6 of 10
if ( p(a)=0.60 ) and ( p(b)=0.20 ), then ( a ) and ( b ) are independent events.
a. ( p(a \text{ and } b)=0 )
b. ( p(a \text{ or } b)=0.80 )
c. ( p(a \text{ or } b)=0.12 )
d. ( p(a \text{ and } b)=0.12 )

Explanation:

Step1: Recall the formula for independent events

For independent events \( A \) and \( B \), \( P(A\ \text{and}\ B)=P(A)\times P(B) \).

Step2: Substitute the given values

Given \( P(A) = 0.60 \) and \( P(B)=0.20 \), then \( P(A\ \text{and}\ B)=0.60\times0.20 = 0.12 \).

Step3: Analyze other options

• Option A: \( P(A\ \text{and}\ B) = 0 \) is for mutually - exclusive events (not independent).
• Option B: \( P(A\ \text{or}\ B)=P(A)+P(B)-P(A\ \text{and}\ B)=0.60 + 0.20-0.12=0.68

eq0.80 \).

• Option C: \( P(A\ \text{or}\ B)

eq0.12 \) (calculated above).

Answer:

D. \( P(A\ \text{and}\ B) = 0.12 \)