To find the probability of picking a yellow or black token from a bag containing various colored tokens, follow these steps:
1. Calculate the Total Number of Tokens:
The bag contains:
- 15 black tokens
- 17 green tokens
- 22 pink tokens
- 29 yellow tokens
Adding these together gives the total number of tokens:
[tex]\[
15 + 17 + 22 + 29 = 83
\][/tex]
2. Determine the Favorable Outcomes:
The favorable outcomes are the scenarios where you pick either a yellow or a black token.
- Number of yellow tokens: 29
- Number of black tokens: 15
So, the total number of favorable outcomes is:
[tex]\[
29 + 15 = 44
\][/tex]
3. Calculate the Probability:
The probability of an event is given by the ratio of the number of favorable outcomes to the total number of outcomes.
[tex]\[
P(\text{yellow or black}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{44}{83}
\][/tex]
The probability of picking a yellow or black token from the bag is:
[tex]\[
P(\text{yellow or black}) = \frac{44}{83} \approx 0.5301204819277109
\][/tex]
This fraction cannot be simplified further, so the answer remains as:
[tex]\[
P(\text{yellow or black}) = \frac{44}{83}
\][/tex]
