you draw two cards from a standard deck of 52 cards, but before you draw the second card, you put the first one back and reshuffle the deck.
a) are the outcomes on the two cards independent? why?
b) find P(3 on 1st card and 10 on 2nd)
c) find P(10 on 1st card and 3 on 2nd)
d) find the probability of drawing a 10 and a 3 in either order.
To find the probability of drawing two specific cards in sequence from a standard deck of 52 cards, including reshuffling the deck after drawing the first card, you can use the concept of conditional probability.
Steps to calculate the probability:
1. Determine the probability of drawing the first card. Since there are 52 cards in the deck and you are drawing one card, the probability of drawing any specific card is 1/52.
2. Reshuffle the deck after drawing the first card, ensuring all cards have an equal chance of being drawn again.
3. Calculate the probability of drawing the second card, taking into account that the first card was replaced and the deck has been reshuffled. Since there are still 52 cards in the deck, the probability of drawing the specific second card is also 1/52.
4. To find the probability of both events occurring (drawing both specific cards in sequence), multiply the individual probabilities. So the overall probability would be (1/52) * (1/52) = 1/2704.
Therefore, the probability of drawing two specific cards in sequence from a standard deck, with reshuffling in between, is 1/2704.