To find the probability that a randomly picked token from the bag is either pink or yellow, we can follow these steps:
1. Count the total number of tokens in the bag:
- There are 15 black tokens.
- There are 17 green tokens.
- There are 22 pink tokens.
- There are 29 yellow tokens.
To find the total number of tokens, we sum these quantities:
[tex]\[
15 + 17 + 22 + 29 = 83
\][/tex]
So, the total number of tokens in the bag is 83.
2. Count the number of desired tokens (pink or yellow):
- There are 22 pink tokens.
- There are 29 yellow tokens.
To find the total number of pink or yellow tokens, we sum these quantities:
[tex]\[
22 + 29 = 51
\][/tex]
So, there are 51 tokens that are either pink or yellow.
3. Calculate the probability:
The probability of an event is given by the number of favorable outcomes divided by the total number of possible outcomes.
Here, the probability [tex]\(P(\text{pink or yellow})\)[/tex] is the number of pink or yellow tokens divided by the total number of tokens:
[tex]\[
P(\text{pink or yellow}) = \frac{\text{Number of pink or yellow tokens}}{\text{Total number of tokens}} = \frac{51}{83}
\][/tex]
4. Convert the fraction to a decimal:
[tex]\[
P(\text{pink or yellow}) \approx 0.6144578313253012
\][/tex]
Thus, the probability that a randomly picked token from the bag is either pink or yellow is approximately [tex]\(0.6145\)[/tex].
