Question

you spin the spinner twice.
what is the probability of landing on a number greater than 6 and then landing on a 6?
simplify your answer and write it as a fraction or whole number.

Explanation:

Step1: Determine the probability of landing on a number greater than 6

There are 4 sections on the spinner. The number greater than 6 is 7. So the probability of landing on a number greater than 6 (i.e., 7) in the first spin is \(P_1=\frac{1}{4}\).

Step2: Determine the probability of landing on 6

The probability of landing on 6 in the second spin is \(P_2 = \frac{1}{4}\).

Step3: Use the multiplication rule for independent events

Since the two spins are independent events, the probability of both events occurring is \(P=P_1\times P_2\). Substitute \(P_1=\frac{1}{4}\) and \(P_2=\frac{1}{4}\) into the formula: \(P=\frac{1}{4}\times\frac{1}{4}\).

Answer:

\(\frac{1}{16}\)