Question

q 22.) veronica rolls a number cube and spins a spinner that is divided into four equal pieces. the number cube contains the numbers 1 - 6 and each section of the spinner has a different shape: triangle, star, circle and square. complete the table to determine the probability that veronica will roll a prime number and spin a star or triangle? express your answer as a decimal.

Explanation:

Step1: Determine prime - numbers on cube

The prime numbers on a cube with numbers 1 - 6 are 2, 3, 5. So there are 3 prime numbers out of 6. The probability of rolling a prime number on the cube is $P(\text{prime})=\frac{3}{6}=\frac{1}{2}$.

Step2: Determine favorable outcomes on spinner

The spinner has 4 equal - pieces with star or triangle being 2 favorable outcomes. The probability of spinning a star or triangle on the spinner is $P(\text{star or triangle})=\frac{2}{4}=\frac{1}{2}$.

Step3: Use multiplication rule for independent events

Since rolling the cube and spinning the spinner are independent events, the probability of both events occurring is the product of their individual probabilities. So $P = P(\text{prime})\times P(\text{star or triangle})$.
Substitute the values: $P=\frac{1}{2}\times\frac{1}{2}=\frac{1}{4}=0.25$.

Answer:

0.25