Question

Three cards are randomly selected from a standard 52-card deck, one at a time, with each card re- placed in the deck before the next one is picked. Find the probability of all three cards are hearts.

Answer 1

`(1)/(4)`

Explanation:

Three cards are randomly selected from a standard 52-card deck.

Number of heart cards in a deck = 13

Each card replaced in the deck before the next one is picked.

Probability of first card is heart =
`P_(1)=(13)/(52)`

After replacement, the probability of second card is heart =
`P_(2)=(13)/(52)`

after replacement, the probability of third card is heart =
`P_(3)=(13)/(52)`

P =
`(13)/(52)` ×
`(13)/(52)` ×
`(13)/(52)`

=
`(39)/(156)`

=
`(1)/(4)`

The probability of all three cards are hearts is
`(1)/(4)`