a card is chosen at random from a deck of 52 cards. it is replaced and a second card is chosen. what is the probability of choosing a king and an ace?
P(2 aces) = (1/13)^2
P(2 kings) = (1/13)^2
P(king and ace) = 8C2/52C2 - 2(1/13)^2 = 0.0152
Answer:
\(\frac{1}{169}\)
Step-by-step explanation:
Total cards = 52
Total ace = 4
So probability of getting ace on first draw = \(\frac{4}{52}\)
Now the card is replaced .
So, Total cards = 52
Total kings = 4
So probability of getting kings on second draw = \(\frac{4}{52}\)
So, the probability of choosing a king and an ace:
= \(\frac{4}{52} \times \frac{4}{52}\)
= \(\frac{1}{169}\)
Hence the probability of choosing a king and an ace is \(\frac{1}{169}\)