If you are dealt two cards successively (with replacement of the first) from a standard 52-card deck, find the probability of getting a heart on the first card and a diamond on the second.
If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.
13/52 * 13/52 = 1/4 * 1/4 = ?
To find the probability of getting a heart on the first card and a diamond on the second, we first need to know how many hearts and diamonds are in a standard 52-card deck.
In a standard deck, there are 13 hearts (Ace to King) and 13 diamonds (Ace to King) for a total of 26 cards.
The probability of getting a heart on the first card is 13/52, because there are 13 hearts out of a total of 52 cards.
After replacing the first card, the deck is still the same, so the probability of getting a diamond on the second card is also 13/52.
To find the probability of both events happening, we multiply the probabilities together:
(13/52) * (13/52) = 169/2704 = 0.0625
Therefore, the probability of getting a heart on the first card and a diamond on the second is 0.0625, or 6.25%.