Find P( ace on 1st card and jack on 2nd)
If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.
If ace not replaced, P = 4/52 * 4/(52-1)
If ace replaced, P = (4/52)^2
To find the probability of getting an ace on the first card and a jack on the second card from a standard deck of 52 playing cards, you need to determine two things:
1. The probability of drawing an ace on the first card.
2. The probability of drawing a jack on the second card, given that an ace was drawn on the first card.
Step 1: Calculate the probability of drawing an ace on the first card.
In a standard deck of 52 playing cards, there are four aces. Therefore, the probability of drawing an ace on the first card is 4/52, which simplifies to 1/13.
Step 2: Calculate the probability of drawing a jack on the second card, given that an ace was drawn on the first card.
After drawing the ace on the first card, there are now 51 cards remaining, with three jacks left in the deck. Therefore, the probability of drawing a jack on the second card, given that an ace was drawn on the first card, is 3/51, which simplifies to 1/17.
Step 3: Multiply the two probabilities together to get the final probability.
To find the probability of both events occurring (drawing an ace on the first card and a jack on the second card), multiply the probabilities obtained in steps 1 and 2:
(1/13) * (1/17) = 1/221
So, the probability of drawing an ace on the first card and a jack on the second card from a standard deck of 52 playing cards is 1/221.
To find the probability of drawing an ace on the first card and a jack on the second card, we need to consider the total number of possibilities and the number of favorable outcomes.
Total Number of Possibilities:
When drawing cards from a standard deck of 52 cards, the first card can be any of the 52 available cards.
Number of Favorable Outcomes:
To draw an ace on the first card, there are 4 aces in a deck. After drawing the first ace, there are 51 cards left in the deck. To draw a jack on the second card, there are 4 jacks remaining in the deck.
Therefore, the number of favorable outcomes is 4 (number of aces) * 4 (number of jacks) = 16.
Putting it all together:
P(ace on 1st card and jack on 2nd) = Number of Favorable Outcomes / Total Number of Possibilities
P(ace on 1st card and jack on 2nd) = 16 / 52 = 4 / 13 ≈ 0.308
So, the probability of drawing an ace on the first card and a jack on the second card is approximately 0.308 or 30.8%.