Question

Given the following probabilities for choosing 2 marbles from a bag of 10 marbles, determine if the events are dependent or independent. P(blue) = 3/10, P(green) = 1/5, P(blue and green) = 3/100

Answer 1

ANSWER

The events are dependent

EXPLANATION

The selection is done without replacement, so the probability of one event occurring affects the other.

For instance, after the first marble is chosen, the sample space reduces and this affects the probability of choosing the second marble.

Also, we were given that,


`P(blue) = (3)/(10)`


`P(green) = (1)/(5)`

and


`P(blue \: \: and \: \: green) = (3)/(100)`

Since

`P(blue \: \: and \: \: green) \\e0`

The events are not mutually exclusive, hence they are dependent.

Also note that, events A and B are independent if and only if


`P(A\:and\:B)=P(A)* P(B).`

Otherwise, A and B are dependent events.

Since


`P(blue \: \: and \: \: green) = (3)/(100) \\e P(blue)* P(green)=(3)/(50)`

The events are dependent.

Answer 2

Dependent events

Explanation:

Given the following probabilities for choosing 2 marbles from a bag of 10 marbles are:-

P(blue) = 3/10, P(green) = 1/5, P(blue and green) = 3/100

We know the fact that two event are independents if we have following:-

P(X and Y) = P(X) times P(Y)

For this problem, we must have P(blue and green) = P(blue) times P(green).

P(blue and green) = (3/10) * (1/5) = 3/50

But given P(blue and green) = 3/100

Since we have 3/100 ≠ 3/50

Hence, the events are not independent events.

So, they are dependent events.