you pick a card at random. without putting the first card back, you pick a second card at random. what is…

Explanation:

Step1: Calculate probability of picking 3 first

There are 3 cards in total. The probability of picking a 3 on the first - draw is $\frac{1}{3}$.

Step2: Calculate probability of picking a number greater than 2 on the second draw given 3 was picked first

Since the first - card (3) is not put back, there are 2 cards left. The numbers greater than 2 among the remaining cards is 0 (because 3 is already drawn). So the probability of picking a number greater than 2 on the second draw given 3 was picked first is $\frac{0}{2}=0$.

Step3: Calculate the joint probability

For two dependent events A and B, the probability of A and B is $P(A\cap B)=P(A)\times P(B|A)$. Here, $P(A)=\frac{1}{3}$ and $P(B|A) = 0$. So $P(A\cap B)=\frac{1}{3}\times0 = 0$.

Answer:

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