A card is drawn from a deck of 52 and recorded. Then the card is replaced and the deck is shiffeled. this process is repeated five times. What is the probability that all five times the car drawn is an ace
prob(ace) = 4/52 = 1/13
prob(5 aces with card replaced each time)
= (1/13)^5 = ....
To find the probability of drawing an ace five times in a row, we need to determine the probability of drawing an ace on each individual draw and then multiply them together.
The deck contains 52 cards, and there are 4 aces in the deck. Therefore, the probability of drawing an ace on any given draw is 4/52, which simplifies to 1/13.
Since the card is replaced after each draw and the deck is shuffled, the probability of drawing an ace remains the same for each draw.
To find the probability of drawing an ace five times in a row, we can multiply the probabilities of each individual draw together:
P(ace on draw 1) * P(ace on draw 2) * P(ace on draw 3) * P(ace on draw 4) * P(ace on draw 5)
= (1/13) * (1/13) * (1/13) * (1/13) * (1/13)
Calculating this expression gives us the probability of all five draws resulting in an ace.