You are dealt a hand of three cards, one at a time. Find the probability that your third card is your first jack.
A) 0.068
B) 0.145
C) 0.127
D) 0.077
E) 0.00018
To find the probability that your third card is your first jack, we need to consider the number of favorable outcomes (getting a jack on the third card) and the number of possible outcomes (all the different ways you can be dealt three cards).
First, let's determine the number of ways you can be dealt three cards from a deck of 52 cards. Since you are dealt one card at a time, there are 52 choices for the first card, 51 choices for the second card, and 50 choices for the third card. So the total number of possible outcomes is 52 * 51 * 50.
Next, let's determine the number of favorable outcomes, which is the number of ways you can get a jack on the third card. There are 4 jacks in a deck of 52 cards, so if your first jack appears on the third card, it means the first two cards are not jacks. So, there are 48 non-jack cards for the first card, 47 non-jack cards for the second card, and 4 jacks for the third card. Therefore, the number of favorable outcomes is 48 * 47 * 4.
Finally, to find the probability, we divide the number of favorable outcomes by the number of possible outcomes. So the probability is (48 * 47 * 4) / (52 * 51 * 50).
Now, let's calculate the probability using a calculator:
(48 * 47 * 4) / (52 * 51 * 50) = 0.077
So the probability that your third card is your first jack is 0.077.
Therefore, the correct answer is D) 0.077.