Question

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 5 and then picking a 3? write your answer as a percentage rounded to the nearest tenth.

Explanation:

Step1: Calculate probability of first - pick

The probability of picking a 5 on the first draw. There are 4 cards in total, so the probability $P_1$ of picking a 5 first is $\frac{1}{4}$ since there is 1 card with the number 5 out of 4 cards.

Step2: Calculate probability of second - pick

After picking a 5 on the first draw (without replacement), there are 3 cards left. The probability $P_2$ of picking a 3 on the second draw is $\frac{1}{3}$ since there is 1 card with the number 3 out of the remaining 3 cards.

Step3: Calculate joint probability

The probability of both events happening is the product of their individual probabilities. So $P = P_1\times P_2=\frac{1}{4}\times\frac{1}{3}=\frac{1}{12}$.

Step4: Convert to percentage

To convert $\frac{1}{12}$ to a percentage, we calculate $\frac{1}{12}\times100\%\approx 8.3\%$.

Answer:

$8.3\%$