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

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 a 2 and then picking a 4? write your answer as a fraction or whole number.

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 a 2 and then picking a 4? write your answer as a fraction or whole number.

Answer

Explanation:

Step1: Calculate probability of picking 2 first

There are 3 cards initially, and 1 card with number 2. So the probability of picking a 2 first is $\frac{1}{3}$.

Step2: Calculate probability of picking 4 second

After picking a 2 first (without replacement), there are 2 cards left. So the probability of picking a 4 second is $\frac{1}{2}$.

Step3: Calculate combined probability

For independent - like (successive without replacement) events, we multiply the probabilities. So the probability of picking a 2 and then a 4 is $\frac{1}{3}\times\frac{1}{2}=\frac{1}{6}$.

Answer:

$\frac{1}{6}$