Question

you pick a card at random. without putting the first card back, you pick a second card at random.
5 6 7 8
what is the probability of picking a 5 and then picking a number greater than 6?
simplify your answer and write it as a fraction or whole number.

Explanation:

Step1: Calculate the probability of picking 5 first

There are 4 cards in total. The probability of picking 5 first is \(P(5)=\frac{1}{4}\).

Step2: Calculate the probability of picking a number greater than 6 second

After picking 5, there are 3 cards left. The numbers greater than 6 are 7 and 8. So the probability of picking a number greater than 6 second is \(P(\text{>6})=\frac{2}{3}\).

Step3: Calculate the combined probability

Since these are two - step dependent events, we use the formula \(P = P_1\times P_2\). So \(P=\frac{1}{4}\times\frac{2}{3}=\frac{1\times2}{4\times3}=\frac{2}{12}=\frac{1}{6}\).

Answer:

\(\frac{1}{6}\)