The probability of event A and event B is the product of the probability of A snd the probability of B given that A has happened. It is written as
P(A and B) = P(A) x P(BIA)
Considering the first option,
We know that
probability = number of favourable outcomes/total number of outcomes
The total number of outcomes is 6
The probability of choosing a 1, P(A) = 1/6
There are 2 blue chips and since the 1 that was chosen was not replaced, the total number of outcomes would be 5. Thus, the probability of choosing a blue chip given that a 1 has been chosen, P(BIA) is 2/5
Thus, the probability of of choosing a 1 and then a blue chip is
1/6 x 2/5 = 1/15
Considering the second option,
The probability of choosing a 1, P(A) = 1/6
there are 3 even numbers. The probability of choosing an even number given that a green chip has been chosen, P(BIA) = 3/5
Thus, the probability of choosing a 1 and then an even number is
1/6 x 3/5 = 1/10
Considering the third option,
The probability of choosing a green chip, P(A) = 1/6
there are 3 chips that are not red after the green chip has been chosen. The probability of choosing a chip that is not red given that a green chip has been chosen, P(BIA) = 3/5
Thus, the probability of choosing green chip and then an even number is
1/6 x 3/5 = 1/10
Considering the fourth option,
The probability of choosing a number less than 2 is , P(A) = 1/6
there are 3 chips that are even numbers. The probability of choosing a chip that is an even number given that a number less than 2 has has been chosen, P(BIA) = 3/5
Thus, the probability of choosing a number less than 2 and then an even number is
1/6 x 3/5 = 1/10
Thus, the only different option is the first one
