Question

A die is rolled and a card is drawn from a standard 52 card deck. What is the possibility that a black ace, or a queen card will be drawn and either a 4 or 5 will be rolled?

Answer 1

Case 1: A die is rolled.

There are total 6 faces on a dice.

So , probability that 4 is rolled is 1/6.

And probability that 5 is rolled is 1/6.

So , possibility that 4 or 5 is rolled is (1/6) + (1/6) =1/3.

Case 2: A card is drawn.

There are 2 black ace cards.

So , possibility that black ace is drawn is 2/52 = 1/26.

And , since there are total 4 Queens,

Possibility that a queen card is drawn is 4/ 52 = 1/13.

So, possibility that black ace or a queen card is drawn

Is (1/26) + (1/13) = 3/26.

Combining both cases,

Required possibility = (1/3)(3/26) = 1/ 26 = 0.03846