Final answer:
To find the probability of drawing a jack and a queen from a deck of 52 cards without replacement, calculate the probability of drawing a jack first and then a queen, as well as the probability of drawing a queen first and then a jack, and add them together.
Step-by-step explanation:
The question asks for the probability of drawing one jack and one queen from a standard deck of 52 cards without replacement. Firstly, there are four jacks and four queens in a deck. To calculate the probability, consider two scenarios: drawing a jack first then a queen, or a queen first then a jack.
For the first scenario, the probability of drawing a jack is 4 out of 52. After drawing the jack, there are 51 cards left in the deck, including four queens, so the probability of then drawing a queen is 4 out of 51. Multiply these probabilities together to get the combined probability for this scenario.
For the second scenario, it's similar: the probability of drawing a queen first is 4 out of 52, and then the probability of drawing a jack with 51 cards left is 4 out of 51. Again, multiply these probabilities together for this scenario.
Finally, add the two probabilities together since either scenario satisfies the condition of drawing one jack and one queen:
- P(Jack first, then Queen) = (4/52) * (4/51)
- P(Queen first, then Jack) = (4/52) * (4/51)
Probability of one jack and one queen = P(Jack first, then Queen) + P(Queen first, then Jack)
Now, simplify and calculate these probabilities to get the final answer.