Question

Question #9d88c

Answer 1

False.

Explanation:

If two events are independent, it means that a result involving one event does not affect the probability of the other.

For example, rolling dice and getting a total of 6 and simultaneously flipping a coin and getting heads are independent events; whether or not I get a sum of 6 on the dice has no influence over whether I get a heads or a tails on the coin and vice versa.

The notation you've shown is that of a conditional probability: `P(A|B)` can be read as "the probability that event A occurs given that event B occurs."

If the two events are independent, it means that the probability of the first event is not influenced by the second event, so the fact that event B has already occurred is irrelevant. Therefore, the probability that event A occurs given event B has occurred where A and B are independent is the same as the probability of A occurring.

`:.` For independent events, `P(A|B)=P(A)`.

Answer 2

B. false.

Explanation:

We say that, events `A and B` are Independent Events, if,

`P(A nn B)=P(A)*P(B).`

Now, `P(A/B)=(P(AnnB))/(P(B)), (P(B) ne 0),`

`={P(A)*cancel(P(B))}/cancel((P(B))),...[because, A & B" are independent],"`

Therefore, `A and B" are independent "rArr P(A/B)=P(A).`

Hence, the statement is B. false.