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
How do I set this problem up?
The first two need to be non-Jacks.
First card = (52-4)/52
With one card gone, the second card = (51-4)/51
The third card needs to be the Jack = 4/50
If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.
To set up this problem, we need to determine the total number of possible outcomes and the number of favorable outcomes.
The total number of possible outcomes can be found using the concept of combinations. Since each card is dealt one at a time, there are 52 options for the first card, 51 options for the second card, and 50 options for the third card. Therefore, the total number of possible outcomes is computed as: 52 * 51 * 50.
Now, let's consider the first jack being the third card, which is our favorable outcome. To calculate the number of favorable outcomes, we can think about it in the following way: for the first two cards, there are 51 non-jack cards to choose from (since there are four jacks in the deck). Then, for the third card, there is only one jack card left in the deck. So, the number of favorable outcomes is computed as: 51 * 50 * 1.
Now, we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes:
Probability = (Number of Favorable Outcomes) / (Total Number of Possible Outcomes)
Substituting the values calculated previously:
Probability = (51 * 50 * 1) / (52 * 51 * 50)
Simplifying the expression, the probability is:
Probability = 1 / 52
Therefore, the correct answer is E) 0.00018, as it represents the probability of the third card being the first jack.