Question

you spin the spinner twice. what is the probability of landing on a number greater than 2 and then landing on a number greater than 3? write your answer as a percentage.

Explanation:

Step1: Determine single - spin probabilities

The spinner has 4 equal sections numbered 1, 2, 3, 4. The probability of landing on a number greater than 2 in a single spin is the number of favorable outcomes (2, which are 3 and 4) divided by the total number of outcomes (4). So the probability of landing on a number greater than 2 in one spin, $P(A)=\frac{2}{4}=\frac{1}{2}$. The probability of landing on a number greater than 3 in a single spin is the number of favorable outcomes (1, which is 4) divided by the total number of outcomes (4). So the probability of landing on a number greater than 3 in one spin, $P(B)=\frac{1}{4}$.

Step2: Use the multiplication rule for independent events

Since the two spins are independent events, the probability of two independent events $A$ and $B$ occurring is $P(A\cap B)=P(A)\times P(B)$. Substitute $P(A)=\frac{1}{2}$ and $P(B)=\frac{1}{4}$ into the formula. So $P(A\cap B)=\frac{1}{2}\times\frac{1}{4}=\frac{1}{8}$.

Step3: Convert to percentage

To convert $\frac{1}{8}$ to a percentage, we use the formula $\text{Percentage}=\frac{1}{8}\times100\%$. $\frac{1}{8}\times100\% = 12.5\%$.

Answer:

12.5%