To find the theoretical probability that Adam will pick a blue marble from the bag, we can proceed as follows:
1. Determine the total number of marbles in the bag:
The bag contains:
- 8 red marbles
- 7 blue marbles
- 6 green marbles
Adding these together gives us the total number of marbles:
[tex]\[
8 + 7 + 6 = 21
\][/tex]
2. Identify the number of favorable outcomes:
In this case, the favorable outcome is picking a blue marble. There are 7 blue marbles in the bag.
3. Calculate the probability:
The probability [tex]\(P\)[/tex] of an event is given by the ratio of the number of favorable outcomes to the total number of possible outcomes. Here, the probability [tex]\(P\)[/tex] of picking a blue marble is:
[tex]\[
P(\text{{blue marble}}) = \frac{\text{{number of blue marbles}}}{\text{{total number of marbles}}}
\][/tex]
Substituting the values, we get:
[tex]\[
P(\text{{blue marble}}) = \frac{7}{21}
\][/tex]
4. Simplify the fraction:
The fraction [tex]\(\frac{7}{21}\)[/tex] can be simplified by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 7:
[tex]\[
\frac{7 \div 7}{21 \div 7} = \frac{1}{3}
\][/tex]
Therefore, the theoretical probability that Adam will pick a blue marble from the bag is:
[tex]\[
\boxed{\frac{1}{3}}
\][/tex]
