To find the probability of rolling a number greater than 3 and spinning red, let's break down the problem into steps.
1. Probability of Rolling a Number Greater than 3:
A standard number cube has six faces with numbers 1 through 6. The numbers greater than 3 are 4, 5, and 6. So the favorable outcomes for rolling a number greater than 3 are 4, 5, and 6.
Therefore, the number of favorable outcomes = 3 (i.e., 4, 5, and 6).
The total number of possible outcomes when rolling the number cube = 6.
Hence, the probability of rolling a number greater than 3 can be calculated as follows:
[tex]\[
\text{Probability of rolling a number greater than 3} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{3}{6} = 0.5
\][/tex]
2. Probability of Spinning Red:
The spinner has two equal-sized sections: Red (R) and Yellow (Y).
Therefore, the number of favorable outcomes for spinning red = 1 (since there is only one red section).
The total number of possible outcomes when spinning the spinner = 2.
Hence, the probability of spinning red can be calculated as follows:
[tex]\[
\text{Probability of spinning red} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{1}{2} = 0.5
\][/tex]
3. Combined Probability of Both Events Happening:
The events of rolling the number cube and spinning the spinner are independent events. To find the combined probability of both events happening, we need to multiply the probabilities of each event.
Therefore, the combined probability of rolling a number greater than 3 and spinning red is given by:
[tex]\[
\text{Combined probability} = \left(\text{Probability of rolling a number greater than 3}\right) \times \left(\text{Probability of spinning red}\right)
\][/tex]
[tex]\[
\text{Combined probability} = 0.5 \times 0.5 = 0.25
\][/tex]
Expressing this combined probability as a fraction:
[tex]\[
0.25 = \frac{1}{4}
\][/tex]
Thus, the probability of rolling a number greater than 3 and spinning red is [tex]\(\frac{1}{4}\)[/tex]. The correct answer is:
A. [tex]\(\frac{1}{4}\)[/tex]
