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 the probability of picking an even number first

There are 3 cards in total (\(3\), \(4\), \(5\)), and only \(1\) even number (\(4\)).
The probability \(P_1=\frac{1}{3}\)

Step2: Calculate the probability of picking an even number second (after picking an even number first)

After picking the first card (which was even), there are \(2\) cards left. Since the first - picked card was even, there are \(0\) even numbers left.
The probability \(P_2 = 0\)

Step3: Calculate the combined probability

For two - step dependent events, the combined probability \(P=P_1\times P_2\)
\(P=\frac{1}{3}\times0 = 0\)

Answer:

\(0\)