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 5 cards in total, and 2 of them (4 and 6) are even numbers. The probability of picking an even - numbered card on the first pick is $\frac{2}{5}$.

Step2: Calculate second - pick probability

Since the first card is not replaced, there are 4 cards left. If the first card was even, then there is 1 even - numbered card left. So the probability of picking an even - numbered card on the second pick given that the first card was even is $\frac{1}{4}$.

Step3: Calculate joint probability

The probability of two independent events $A$ and $B$ (in this case, picking an even number first and then picking an even number second) is $P(A)\times P(B)$. So the probability is $\frac{2}{5}\times\frac{1}{4}=\frac{2}{20}=\frac{1}{10}$.

Answer:

$\frac{1}{10}$