a card is chosen at a random from a deck of 52 cards. it is then replaced and a second card is chosen. what is the probability of getting a jack and then an eight?
Calculate the probability of drawing a jack from a full deck
There are 4 jacks in a deck of 52 cards
P(J) = 4/52
P(J) = 1/13 <-- We simplify 4/52 by dividing top and bottom of the fraction by 4
Calculate the probability of drawing an eight from a full deck
There are 4 eights in a deck of 52 cards. We replaced the first card giving us 52 cards to choose from.
P(8) = 4/52
P(8) = 1/13 <-- We simplify 4/52 by dividing top and bottom of the fraction by 4
Since each event is independent, we multiply:
P(J, 8) = P(J) * P(8)
P(J, 8) = 1/13 * 1/13
P(J, 8) = 1/169
Calculate the probability of drawing a jack from a full deck
There are 4 jacks in a deck of 52 cards
P(J) = 4/52
P(J) = 1/13 <-- We simplify 4/52 by dividing top and bottom of the fraction by 4
Calculate the probability of drawing an eight from a full deck
There are 4 eights in a deck of 52 cards. We replaced the first card giving us 52 cards to choose from.
P(8) = 4/52
P(8) = 1/13 <-- We simplify 4/52 by dividing top and bottom of the fraction by 4
Since each event is independent, we multiply:
P(J, 8) = P(J) * P(8)
P(J, 8) = 1/13 * 1/13
P(J, 8) = 1/169