Question

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 an 8 and then picking a number greater than 5? write your answer as a fraction or whole number.

Explanation:

Step1: Calculate probability of picking 8 first

There are 4 cards. The probability of picking 8 on the first - pick is $\frac{1}{4}$.

Step2: Calculate probability of picking a number greater than 5 on the second pick

After picking 8 on the first pick, there are 3 cards left. The numbers greater than 5 among the remaining cards are 6 and 7, so there are 2 such cards. The probability of picking a number greater than 5 on the second pick given that 8 was picked first is $\frac{2}{3}$.

Step3: Use the multiplication rule for independent - dependent events

The probability of both events occurring is the product of their probabilities. So the probability of picking 8 first and then a number greater than 5 is $\frac{1}{4}\times\frac{2}{3}=\frac{2}{12}=\frac{1}{6}$.

Answer:

$\frac{1}{6}$