To find the estimated probability of choosing a white marble from the bag, follow these steps:
1. Determine the number of times a white marble was chosen: According to the data, Nick chose a white marble 48 times out of the total trials.
2. Determine the total number of trials: The problem states that he performed 100 trials in total.
3. Calculate the probability: The probability [tex]\( P \)[/tex] of choosing a white marble is the number of times a white marble was chosen divided by the total number of trials. Therefore,
[tex]\[
P(\text{white}) = \frac{\text{Number of times a white marble was chosen}}{\text{Total number of trials}}
\][/tex]
which gives us:
[tex]\[
P(\text{white}) = \frac{48}{100}
\][/tex]
4. Simplify the fraction: To simplify [tex]\(\frac{48}{100}\)[/tex], we need to find the greatest common divisor (GCD) of 48 and 100.
- The GCD of 48 and 100 is 4.
So, divide both the numerator and the denominator by 4:
[tex]\[
\frac{48 \div 4}{100 \div 4} = \frac{12}{25}
\][/tex]
So, the estimated probability of choosing a white marble from the bag, in its simplest form, is [tex]\(\frac{12}{25}\)[/tex].
The correct answer is:
A. [tex]\(\frac{12}{25}\)[/tex]
