Question

Events M and N are independent events. In this scenario, if P(M) = 0.46 and P(M and N) = 0.138, then P(N) = .

Answer 1

For two independent events A and B: Prob (A ∩ B) = Prob (A) Prob (B)

Then, P(M and N) = P(M)*P(N)⇒P(N) = P(M and N) / P(M) = 0.138 / 0.46 = 0.3

Answer 2

Value of P(N) is, 0.3

Explanation:

As per the given statement:

Events M and N are independent events.

By definition of independency ;

`P(M \text{and} N) = P(M) * P(N)`

Also,in this scenario, if P(M) = 0.46 and P(M and N) = 0.138

Substitute the given values in [1] to solve for P(N);

`0.138=0.46 * P(N)`\

Divide both sides by 0.46 we get;

`(0.138)/(0.46) = (0.46 * P(N))/(0.46)`

Simplify:

`P(N) = 0.3`

Therefore, the value of P(N) = 0.3