A deck contains 7 cards numbered 1 through 7 . A card is randomly chosen from the deck. The card is then put back into the deck. The deck is shuffled. Then another random selection is made.
What is the probability of getting any particular card in the first draw?
The probability of getting any particular card in the first draw is 1 in 7, or 1/7.
What is the probability of getting any particular card in the second draw?
Since the card was put back into the deck, the probabilities remain the same. So, the probability of getting any particular card in the second draw is also 1 in 7, or 1/7.
What is the probability of getting the same card in both draws?
To find the probability of getting the same card in both draws, multiply the probabilities of getting any particular card in the first draw and second draw.
Probability of getting the same card in both draws = (1/7) * (1/7) = 1/49.
What is the probability of getting different cards in the two draws?
Since there are only two possibilities, getting the same card or getting different cards, the probability of getting different cards is the complement of the probability of getting the same card.
Probabilty of getting different cards in the two draws = 1 - (Probability of getting the same card in both draws) = 1 - (1/49) = 48/49.