Question

you pick a card at random. without putting the first card back, you pick a second card at random. 1 2 3 4 what is the probability of picking a 3 and then picking a divisor of 24? write your answer as a decimal.

Explanation:

Step1: Calculate the probability of picking 3 first

There are 4 cards in total. The probability of picking 3 is \(P(3)=\frac{1}{4}\) since there is 1 card with 3 out of 4 cards.

Step2: Calculate the probability of picking a divisor of 24 second

After picking 3, there are 3 cards left. The divisors of 24 among 1, 2, 4 are 1, 2, 4. So there are 3 divisors of 24 among the remaining 3 cards. The probability of picking a divisor of 24 given that 3 was picked first is \(P(\text{divisor of }24|3)=\frac{3}{3} = 1\)

Step3: Use the multiplication rule for dependent events

The multiplication rule for dependent events is \(P(A\cap B)=P(A)\times P(B|A)\). Here \(A\) is the event of picking 3 and \(B\) is the event of picking a divisor of 24. So \(P = \frac{1}{4}\times1=\frac{1}{4}=0.25\)

Answer:

\(0.25\)