Question

you spin the spinner twice.
what is the probability of landing on a prime number and then landing on a number greater than 1?
simplify your answer and write it as a fraction or whole number.

Explanation:

Step1: Determine the probability of landing on a prime number

The numbers on the spinner are \(1\), \(2\), \(3\), \(4\). Prime numbers among them are \(2\) and \(3\). So there are \(2\) prime numbers out of \(4\) total numbers.
The probability of landing on a prime number \(P(\text{prime})=\frac{2}{4}=\frac{1}{2}\)

Step2: Determine the probability of landing on a number greater than \(1\)

The numbers greater than \(1\) are \(2\), \(3\), \(4\). So there are \(3\) numbers greater than \(1\) out of \(4\) total numbers.
The probability of landing on a number greater than \(1\) \(P(> 1)=\frac{3}{4}\)

Step3: Use the multiplication rule for independent events

Since the two spins are independent events, the probability of both events occurring is \(P = P(\text{prime})\times P(>1)\)

$$P=\frac{1}{2}\times\frac{3}{4}=\frac{3}{8}$$

Answer:

\(\frac{3}{8}\)