To find the probability of picking a number greater than 3 and then picking another number greater than 3 when selecting two cards at random, we need to consider the total number of possible outcomes and the number of favorable outcomes.
1. Total number of outcomes:
- When picking a card at random and then putting it back, the total number of outcomes for each pick is the same. Since there are 52 cards in a standard deck, the total number of outcomes for each pick is 52.
2. Number of favorable outcomes for picking a number greater than 3:
- In a standard deck of 52 cards, there are 4 cards greater than 3 in each suit (4, 5, 6, 7, 8, 9, 10, J, Q, K, A). So, there are a total of 13 cards greater than 3 in each suit.
- Since there are 4 suits (hearts, diamonds, clubs, spades), the total number of cards greater than 3 in the deck is 13 x 4 = 52.
3. Probability calculation:
- The probability of picking a number greater than 3 in the first draw is 52/52 (since all cards are greater than 3).
- After replacing the card, the probability of picking a number greater than 3 in the second draw is also 52/52.
Therefore, the probability of picking a number greater than 3 and then picking another number greater than 3 is:
(52/52) * (52/52) = 1 * 1 = 1
The probability is 1, which means it is certain that you will pick a number greater than 3 in both draws when selecting two cards at random.
