Question

In a standard deck of playing cards, one-fourth of the cards are hearts.

There are 3 decks of cards. One card is dealt from each deck. What is
the probability that all 3 cards are hearts?
A
12
B
1
24
C
1
32
D
1
64

Answer 1

`\sf D) \quad (1)/(64)`

Explanation:

`\sf Probability\:of\:an\:event\:occurring = (Number\:of\:ways\:it\:can\:occur)/(Total\:number\:of\:possible\:outcomes)`

Probability of drawing a heart from one deck:

`\sf \implies P(heart)=(1)/(4)`

Therefore, probability of drawing a heart from each of 3 decks:

`\sf \implies P(heart)\:and\:P(heart)\:and\:P(heart)=(1)/(4) * (1)/(4) * (1)/(4)=(1)/(64)`