To solve this problem, we need to determine the probability of not picking a pink token from the bag. We will proceed step-by-step to find the solution.
Step 1: Calculate the total number of tokens in the bag.
The bag contains:
- 15 black tokens
- 17 green tokens
- 22 pink tokens
- 29 yellow tokens
Summing these up gives us the total number of tokens:
[tex]\[ 15 + 17 + 22 + 29 = 83 \][/tex]
Thus, there are 83 tokens in total.
Step 2: Calculate the probability of picking a pink token.
The number of pink tokens is 22, and the total number of tokens is 83. The probability of picking a pink token is the ratio of the number of pink tokens to the total number of tokens:
[tex]\[ P(\text{pink}) = \frac{22}{83} \][/tex]
Step 3: Calculate the probability of not picking a pink token.
The probability of not picking a pink token is 1 minus the probability of picking a pink token:
[tex]\[ P(\text{not pink}) = 1 - P(\text{pink}) \][/tex]
Substituting the value we found for [tex]\(P(\text{pink})\)[/tex]:
[tex]\[ P(\text{not pink}) = 1 - \frac{22}{83} \][/tex]
Step 4: Simplify the probability of not picking a pink token.
Perform the subtraction:
[tex]\[ P(\text{not pink}) = 1 - \frac{22}{83} = \frac{83}{83} - \frac{22}{83} = \frac{83 - 22}{83} = \frac{61}{83} \][/tex]
Thus, the probability of not picking a pink token is:
[tex]\[ P(\text{not pink}) = \frac{61}{83} \approx 0.7349397590361446 \][/tex]
So, the simplified fraction representing the probability of not picking a pink token is:
[tex]\[ \boxed{\frac{61}{83}} \][/tex]
