Your friend has two standard decks of 52 playing cards and asks you to randomly draw one card from each deck. what is the probability that you will draw two spades? express your first answer as a fraction in simplest form, and round your percent answer to the nearest hundredth.
Accepted Solution
A:
There are 13 spades in one deck, so the probability to draw a spade from the first deck is [tex] P_1=\frac{1}{4} [/tex]
Similarly, the probability to draw a spade from the second deck is [tex] P_2=\frac{1}{4} [/tex]
The probability that both events occur (so, the probability we have to draw two spades from the two decks) is the product of the two probabilities, so: [tex]P=P_1 \cdot P_2 = \frac{1}{4} \cdot \frac{1}{4}= \frac{1}{16} [/tex]