Certainly! Let's break down the problem step-by-step to determine the experimental probability that Brandy will roll a strike in the first frame of the next game.
1. Understanding the problem:
Brandy has bowled a total of 10 frames. Out of these 10 frames, she managed to roll a strike in 6 of them. We are asked to find the experimental probability that she will roll a strike in the first frame of the next game.
2. Determining the number of successful outcomes:
The number of successful outcomes refers to the number of times Brandy rolled a strike. According to the problem, Brandy rolled a strike in 6 frames. So, the number of successful outcomes is 6.
3. Determining the total number of trials:
The total number of trials is the total number of frames bowled. In this case, Brandy bowled a total of 10 frames.
4. Calculating the experimental probability:
The experimental probability of an event occurring is given by the formula:
[tex]\[
\text{Experimental Probability} = \frac{\text{Number of Successful Outcomes}}{\text{Total Number of Trials}}
\][/tex]
Substituting the values we have:
[tex]\[
\text{Experimental Probability} = \frac{6}{10}
\][/tex]
5. Simplifying the fraction:
The fraction [tex]\(\frac{6}{10}\)[/tex] can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 2:
[tex]\[
\frac{6 \div 2}{10 \div 2} = \frac{3}{5}
\][/tex]
6. Converting the fraction to a decimal:
If we convert the fraction [tex]\(\frac{3}{5}\)[/tex] to a decimal, we get:
[tex]\[
\frac{3}{5} = 0.6
\][/tex]
Therefore, the experimental probability that Brandy will roll a strike in the first frame of the next game is [tex]\(0.6\)[/tex] or [tex]\(60\%\)[/tex].
In summary:
- Number of strikes: 6
- Total frames bowled: 10
- Experimental probability: [tex]\(0.6\)[/tex] or [tex]\(60\%\)[/tex]
So, there is a 60% chance that Brandy will roll a strike in the first frame of the next game.
