Five cards — the ten, jack, queen, king and ace of diamonds, are well-shuffled with their face downwards. One card is then picked up at random.
(i) What is the probability that the card is the queen?
(ii) If the queen is drawn and put aside, what is the probability that the second card picked up is (a) an ace? (b) a queen?
Given:
We have 5 cards — the Ten, Jack, Queen, King, and Ace of Diamonds, shuffled well with the face down.
(i) Probability that the card drawn is the Queen:
There is only 1 Queen out of the 5 cards.
- Favorable outcome = 1 (Queen)
- Total outcomes = 5 cards
The probability is:
P(Queen) = 1/5
(ii) If the Queen is drawn and set aside, what is the probability that the second card picked is:
After the Queen is drawn, only 4 cards remain: Ten, Jack, King, and Ace.
- Total outcomes left = 4 remaining cards
(a) Probability that the second card is an Ace:
There is 1 Ace among the remaining 4 cards.
- Favorable outcome = 1 (Ace)
- Total outcomes left = 4
The probability is:
P(Ace) = 1/4
(b) Probability that the second card is a Queen:
Since the Queen has already been drawn and set aside, there is no Queen left.
- Favorable outcome = 0 (no Queen left)
- Total outcomes left = 4
The probability is:
P(Queen) = 0/4 = 0