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 2 first

There are 4 cards in total. The probability of picking a 2 on the first - draw is $\frac{1}{4}$.

Step2: Calculate probability of picking a divisor of 24 second

After picking a 2 on the first draw, there are 3 cards left. The divisors of 24 among the remaining 3 cards are 1, 3, 4. So there are 3 divisors of 24 among the remaining 3 cards, and the probability of picking a divisor of 24 on the second draw given that a 2 was picked first is $\frac{3}{3} = 1$.

Step3: Calculate the joint - probability

The probability of two dependent events $A$ and $B$ is $P(A\cap B)=P(A)\times P(B|A)$. Here, $A$ is the event of picking a 2 first and $B$ is the event of picking a divisor of 24 second. So $P = \frac{1}{4}\times1=\frac{1}{4}$.

Step4: Convert to percentage

To convert $\frac{1}{4}$ to a percentage, we multiply by 100. $\frac{1}{4}\times100 = 25%$.

Answer:

25%