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…

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?\no $\frac{1}{64}$\no $\frac{1}{56}$\no $\frac{3}{32}$\no $\frac{3}{28}$

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?\no $\frac{1}{64}$\no $\frac{1}{56}$\no $\frac{3}{32}$\no $\frac{3}{28}$

Answer

Answer:

B. $\frac{1}{56}$

Explanation:

Step1: Calculate total number of cards

There are $2 + 2+3 + 1=8$ cards.

Step2: Calculate probability of pulling a 3 first

There are 3 cards with number 3. So probability $P(3)=\frac{3}{8}$.

Step3: Calculate probability of pulling a 2 second (without replacement)

After pulling a 3, there are 7 cards left. There are 2 cards with number 2. So probability $P(2)=\frac{2}{7}$.

Step4: Calculate combined probability

By multiplication - rule of probability for dependent events, $P = \frac{3}{8}\times\frac{2}{7}=\frac{6}{56}=\frac{1}{56}$.