Question

Draw three cards from a deck of regular playing cards, replacing the cards and shuffling the cards between draws. Compute the probability of drawing a heart, a ten, and a club in that order.

Answer 1

The probability of drawing a heart, a ten and a club in that order is
`4.8077^-^3=0.0048077`.

Explanation:

We know that a standard deck of cards has 52 cards and 4 suits, and each suit has 13 cards. Since the cards are replaced and shuffled before drawing a new one, we know that the events are independent to each other.

First, we compute the probability of each event separately:

`P(Heart)= 13/52=0.25\\  P(Ten) = 4/52=0.0769\\ P(Club) = 13/52 = 0.25`

Next, we compute the probability of the compound event of drawing a heart, a ten and a club in that order which is given by:

`P(H\cap Ten \cap C)= P(H)* P(Ten) * P(C)`

`P(H\cap Ten \cap C)= 13/52 * 4/52 * 13/52 = 4.8077^-^3=0.0048077`