To determine the value of [tex]\( x \)[/tex] such that [tex]\(\frac{1}{x}\)[/tex] is the experimental probability of rolling a 3, we need to follow several steps:
1. Calculate the total number of rolls:
- Number of times a 1 was rolled: 4
- Number of times a 2 was rolled: 6
- Number of times a 3 was rolled: 5
- Number of times a 4 was rolled: 7
- Number of times a 5 was rolled: 3
- Number of times a 6 was rolled: 5
Summing these frequencies gives the total number of rolls:
[tex]\[
4 + 6 + 5 + 7 + 3 + 5 = 30
\][/tex]
2. Calculate the frequency of rolling a 3:
The frequency of rolling a 3 is given directly in the table as 5.
3. Calculate the experimental probability of rolling a 3:
The probability, [tex]\( P(3) \)[/tex], is given by the frequency of 3 divided by the total number of rolls.
[tex]\[
P(3) = \frac{\text{frequency of 3}}{\text{total number of rolls}} = \frac{5}{30} = \frac{1}{6}
\][/tex]
4. Determine [tex]\( x \)[/tex] such that [tex]\( \frac{1}{x} = P(3) \)[/tex]:
We know [tex]\( P(3) = \frac{1}{6} \)[/tex]. Therefore, we need [tex]\( x \)[/tex] such that:
[tex]\[
\frac{1}{x} = \frac{1}{6}
\][/tex]
By comparing both sides, we see that:
[tex]\[
x = 6
\][/tex]
Thus, the answer is [tex]\( x = 6 \)[/tex].
