Question

you pick a card at random. without putting the first card back, you pick a second card at random.
2 3 4
what is the probability of picking an odd number and then picking an odd number?
simplify your answer and write it as a fraction or whole number.

Explanation:

Step1: Calculate the probability of picking an odd number first

There are 3 cards in total (\(2\), \(3\), \(4\)), and 1 odd - numbered card (\(3\)). The probability of picking an odd number first, \(P(A)=\frac{1}{3}\).

Step2: Calculate the probability of picking an odd number second

After picking the first card (an odd number), there are 2 cards left. Since the first odd - numbered card is already picked, there are 0 odd - numbered cards left among the remaining 2 cards. The probability of picking an odd number second given that an odd number was picked first, \(P(B|A) = 0\).

Step3: Use the formula for the probability of two dependent events \(P(A\cap B)=P(A)\times P(B|A)\)

Substitute \(P(A)=\frac{1}{3}\) and \(P(B|A) = 0\) into the formula: \(P(A\cap B)=\frac{1}{3}\times0=0\)

Answer:

\(0\)