True or False When A and B are independent PAPB PA and BPBAP

True or False

When A and B are independent, P(A)=P(B).

P(A and B)=P(B|A)P(B).

Solution

FALSE: When A and B are independent, P(A)=P(B).

Ex. Getting a 6 on a roll of die has probability of 1/6, a head in a coin toss is 1/2. These are independent events as they don\'t influence each other.

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FALSE: P(A and B)=P(B|A)P(B).

Instead, it should be

P(A and B) = P(A|B)P(B).