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 an even number and then picking an even number? simplify your answer and write it as a fraction or whole number.

Explanation:

Step1: Calculate first - pick probability

There are 2 even numbers (2 and 4) out of 5 cards. So the probability of picking an even number on the first pick is $\frac{2}{5}$.

Step2: Calculate second - pick probability

After picking an even number on the first pick without replacement, there is 1 even number left out of 4 remaining cards. So the probability of picking an even number on the second pick is $\frac{1}{4}$.

Step3: Calculate combined probability

Since these are dependent events, we multiply the probabilities of each event. So the probability of picking an even number and then another even number is $\frac{2}{5}\times\frac{1}{4}=\frac{2}{20}=\frac{1}{10}$.

Answer:

$\frac{1}{10}$