Event A represents the act of drawing a rank of eight from a standard deck of 52 cards, if B represents the event of drawing any diamond after the first card has been replaced into the deck, what is the probability of A and B.
By "rank of eight" I assume you mean any eight card. The probability of that happening on the first draw is 4/52.
Since tha first card drawn is then replaced in the deck, the probability of drawing a diamond in the next draw is 13/52, and you just multiply the two probabilities.
The answer would therefore be (4/52)*(13/52) = 1/52.
To find the probability of A and B occurring, we need to multiply the probabilities of each event happening.
Let's break down each event and calculate their individual probabilities:
Event A: Drawing a rank of eight from a standard deck of 52 cards
A standard deck of cards has 4 eights (one in each suit), so there are 4 favorable outcomes out of 52 possible outcomes.
Therefore, the probability of drawing a rank of eight is 4/52, which simplifies to 1/13.
Event B: Drawing any diamond after the first card has been replaced into the deck
After drawing the first card, there are still 52 cards in the deck, including 13 diamonds.
Therefore, the probability of drawing a diamond is 13/52, which simplifies to 1/4.
Note: The fact that the first card was replaced ensures that the probability remains the same for the second card.
Now, to find the probability of A and B occurring together, we multiply the probabilities:
P(A and B) = P(A) * P(B)
P(A and B) = (1/13) * (1/4)
P(A and B) = 1/52
So, the probability of both event A and event B occurring is 1/52.