Let's solve the problem step-by-step:
1. Determine the Total Number of Tokens:
- The bag contains different colored tokens: 15 black, 17 green, 22 pink, and 29 yellow.
- To find the total number of tokens, add them all together:
[tex]\[
15 \, \text{(black)} + 17 \, \text{(green)} + 22 \, \text{(pink)} + 29 \, \text{(yellow)}
\][/tex]
- Adding these, we get:
[tex]\[
15 + 17 + 22 + 29 = 83
\][/tex]
- So, there are 83 tokens in total.
2. Calculate the Number of Non-Black Tokens:
- To find the number of non-black tokens, consider only the green, pink, and yellow tokens.
- Add the counts of these non-black tokens:
[tex]\[
17 \, \text{(green)} + 22 \, \text{(pink)} + 29 \, \text{(yellow)}
\][/tex]
- Adding these, we get:
[tex]\[
17 + 22 + 29 = 68
\][/tex]
- So, there are 68 non-black tokens.
3. Calculate the Probability of Picking a Non-Black Token:
- The probability that a randomly picked token is not black can be calculated as the ratio of non-black tokens to the total number of tokens.
- Thus, the probability [tex]\( P(\text{not black}) \)[/tex] is:
[tex]\[
P(\text{not black}) = \frac{\text{Number of non-black tokens}}{\text{Total number of tokens}} = \frac{68}{83}
\][/tex]
- This fraction simplifies to approximately:
[tex]\[
P(\text{not black}) \approx 0.8193
\][/tex]
Hence, the probability that a token picked at random is not black is approximately [tex]\( \boxed{0.8192771084337349} \)[/tex].
