Question

suppose a number cube labeled from 1 to 6 is rolled and the spinner below is spun one time. what is the probability of rolling a number less than 4 and spinning a consonant?
value: 3
a. 3/20
b. 3/5
c. 3/10
d. 1/5

Explanation:

Step1: Calculate probability of rolling a number less than 4

The numbers less than 4 on a 1 - 6 number cube are 1, 2, 3. So there are 3 favorable outcomes out of 6 total outcomes. The probability $P_1=\frac{3}{6}=\frac{1}{2}$.

Step2: Calculate probability of spinning a consonant

Assume vowels are a, e, i, o, u. If the spinner has 5 sections labeled A, B, C, D, E, and vowels are A and E, then the consonants are B, C, D. So there are 3 favorable outcomes out of 5 total outcomes. The probability $P_2 = \frac{3}{5}$.

Step3: Calculate the combined probability

Since the two events (rolling the cube and spinning the spinner) are independent, the probability of both events occurring is the product of their individual probabilities. So $P = P_1\times P_2=\frac{1}{2}\times\frac{3}{5}=\frac{3}{10}$.

Answer:

C. $\frac{3}{10}$