What is the probability of rolling a 3 on a number cube and choosing a heart from a deck of cards

Question

Compound probability & dependent event

Answer 1

A number cube is a 6 sided die, so the probability of rolling a 3 is 1/6. There are 52 cards in a standard poker deck, and there are 4 suits. Since each suit has the same number of cards, there is a 13/52 or 1/4 chance of drawing a heart. Since the number we roll on the die doesn't change the deck of cards, we multiply the 2 numbers to get (1/6)*(1/4) or a 1/24 chance of rolling a 3 and drawing a heart.

Answer 2

P(A and B)=P(A)*P(B)

Since there is one 3 on a number cube of six numbers the probability of rolling a 3 is 1 out of 6 or 1/6 so

P(rolling a 3)=1/6

Since there are 4 suits in a deck of 52 cards (hearts, spades, diamonds, and clubs), therefore there are 13 cards of each suit in 52 cards. The probability of drawing a heart from a deck of cards is 13 out of 52 or 13/52 which simplifies to 1/4. So

P(drawing a heart)=1/4

then P(rolling a 3 and drawing a heart)=1/6 * 1/4 =1/24

Answer 3

Hi Ahsyia!

The probability of rolling a 3 on a cube is 1/6, let's call that P₁

The probability of choosing a heart in a deck of cards is 1/4. Let's call that P₂

As the events are independents, you must do:

P = P₁*P₂

P = 1/24