Question

hiro has a stack of cards with one number from the set 1, 1, 2, 2, 3, 3, 3, 4 written on each card. what is the probability that he pulls out a 3 first and then pulls out a 2 without replacing them?
1/64
1/56
1/32
1/28

Explanation:

Step1: Calculate probability of pulling a 3 first

There are 8 cards in total and 3 cards with the number 3. So the probability of pulling a 3 first is $\frac{3}{8}$.

Step2: Calculate probability of pulling a 2 second

After pulling a 3 first (without replacement), there are 7 cards left. There are 2 cards with the number 2. So the probability of pulling a 2 second is $\frac{2}{7}$.

Step3: Calculate combined probability

The probability of both events happening is the product of their individual probabilities. So $P=\frac{3}{8}\times\frac{2}{7}=\frac{6}{56}=\frac{3}{28}$.

Answer:

$\frac{3}{28}$