Alisha conducted an experiment in which a spinner landed on green 7 times. If the experimental probability of the spinner landing on green is [tex]$\frac{1}{5}$[/tex], how many trials did Alisha perform?

A. 30
B. 35
C. 45
D. 50



Answer :

To solve this problem, let's use the information given:

- Alisha observed that the spinner landed on green 7 times.
- The experimental probability of landing on green is [tex]\(\frac{1}{5}\)[/tex].

Let's denote the total number of trials by [tex]\( T \)[/tex].

The experimental probability is calculated as the ratio of the number of successful outcomes (landing on green) to the total number of trials:

[tex]\[ \text{Experimental Probability} = \frac{\text{Number of Successful Outcomes}}{\text{Total Number of Trials}} \][/tex]

Given that the experimental probability is [tex]\(\frac{1}{5}\)[/tex] and the number of successful outcomes is 7, we can set up the following equation:

[tex]\[ \frac{1}{5} = \frac{7}{T} \][/tex]

To find [tex]\( T \)[/tex], we need to solve for [tex]\( T \)[/tex]. We can do this by cross-multiplying to get:

[tex]\[ 1 \cdot T = 5 \cdot 7 \][/tex]

Simplifying the right-hand side, we get:

[tex]\[ T = 35 \][/tex]

Therefore, the total number of trials Alisha performed is:

[tex]\[ \boxed{35} \][/tex]