you pick a card at random. without putting the first card back, you pick a second card at random. what is…

you pick a card at random. without putting the first card back, you pick a second card at random. what is the probability of picking a 3 and then picking a 1? write your answer as a fraction or whole number.

you pick a card at random. without putting the first card back, you pick a second card at random. what is the probability of picking a 3 and then picking a 1? write your answer as a fraction or whole number.

Answer

Explanation:

Step1: Calculate probability of first - pick

The probability of picking a 3 on the first pick is $\frac{1}{4}$ since there is 1 card with 3 out of 4 total cards.

Step2: Calculate probability of second - pick

After picking a 3 on the first pick and not replacing it, there are 3 cards left. The probability of picking a 1 on the second pick is $\frac{1}{3}$.

Step3: Calculate joint - probability

Since these are dependent events, the probability of both events occurring is the product of their individual probabilities. So $P=\frac{1}{4}\times\frac{1}{3}=\frac{1}{12}$.

Answer:

$\frac{1}{12}$