Question

you pick a card at random, put it back, and then pick another card at random. what is the probability of picking a number greater than 3 and then picking a number less than 3? write your answer as a percentage.

Explanation:

Step1: Calculate probability of first - pick

There are 4 numbers greater than 3 (4 and 5) out of 5 numbers. So the probability of picking a number greater than 3 in the first pick is $\frac{4}{5}$.

Step2: Calculate probability of second - pick

There are 2 numbers less than 3 (2) out of 5 numbers. So the probability of picking a number less than 3 in the second pick is $\frac{2}{5}$.

Step3: Calculate combined probability

Since the two picks are independent events, we multiply the probabilities of each event. The combined probability is $\frac{4}{5}\times\frac{2}{5}=\frac{8}{25}$.

Step4: Convert to percentage

To convert $\frac{8}{25}$ to a percentage, we use the formula $\frac{8}{25}\times100\% = 32\%$.

Answer:

32%