Question

If `"P"(Q) = 4/7` and `"P"(R) = 1/2`, and Q and R are independent events, then what is `"P"(Q nn R)`?

Answer 1

`P(Q nn R) = P(Q) xx P(R)`
`color(white)(P(Q nn R)) = 2/7`

Explanation:

If Q and R are independent, then the probability of the event that both Q and R occur is the product of the probabilities of the two events happening on their own.

Independent events are two events that do not influence each other. In other words, the outcome of one event does not depend on the outcome of the other. A good simple example is if F is the event that a coin toss comes up heads and G is the event that a die roll comes up 3. Just because a coin toss comes up heads, that doesn't change the chance of us rolling a 3 on the die.

Since the probability of tossing a head is `1/2` and the probability of rolling a 3 is `1/6`, we have the probability of getting both a heads and a 3 as `1/2 xx 1/6`, or `1/12`.

Similarly,

`P(Q nn R) = P(Q) xx P(R)`

`color(white)(P(Q nn R)) = 4/7 xx 1/2`

`color(white)(P(Q nn R)) = 4/14`

`color(white)(P(Q nn R)) = 2/7`.