From a 52-card deck a card is drawn and then replaced. After the deck is shuffled, a second card is drawn. Find the probability of each event.
a) both cards are clubs.
PLEASE SHOW ALL WORK!
First you have to answer how many clubs are in a deck of 52 cards!! Then you put that number over 52!
(13/52)(13/52)
=(1/4)(1/4)
= 1/16
you eat out my scrodom and bite my choad
To find the probability of each event, we need to determine the number of favorable outcomes and the total number of possible outcomes.
a) To find the probability that both cards drawn are clubs:
Step 1: Determine the number of favorable outcomes.
In a standard deck of cards, there are 13 clubs (since there are 13 cards of each suit). When the first card is drawn and replaced, it does not affect the probabilities of the cards being drawn again. So the probability of drawing a club on the first draw is 13/52.
Step 2: Determine the total number of possible outcomes.
Since the first card is replaced, the deck remains the same for the second draw. Therefore, the total number of possible outcomes is still 52.
Step 3: Calculate the probability.
The probability of both cards being clubs is the product of the probabilities of each individual event. So:
P(both cards are clubs) = P(first card is a club) * P(second card is a club)
P(both cards are clubs) = (13/52) * (13/52)
P(both cards are clubs) = 169/2704
Simplifying the fraction, we get:
P(both cards are clubs) ≈ 0.0625
Therefore, the probability of both cards drawn being clubs is approximately 0.0625 or 6.25%.