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Chapter 3: Q3.8 (page 184)

Let event A = learning Spanish. Let event B = learning German. Then A AND B = learning Spanish and German.Suppose P(A) = 0.4 and P(B) = 0.2. P(A AND B) = 0.08. Are events A and B independent? Hint: You must show ONE of the following:

• P(A|B) = P(A)

• P(B|A) = P(B)

• P(A AND B) = P(A)P(B)

Short Answer

Expert verified

Yes, A and B are independent events.

Step by step solution

01

Independent Events - Basic Concept 

Two events are independent, when occurrence or non occurrence of an event doesn't effect the probability of occurrence of the other event.

For example : Rolling a dice twice, getting a head or tail at once is independent of getting a head or tail for second time.

02

Solution 

In case of Independent Events, Probability of both events A & B = Probability of Event A x Probability of Event B ; ie P(AANDB)=P(A)P(B)

  • In given case - event A = learning German has probability = 0.4 , event B = learning German = 0.2

Probability (A & B) ie learning both languages =P(A)xP(B)=0.4x0.2=0.8

Hence, these events are independent.

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