Final answer:
To calculate the probability that Bob will draw $15 in tokens, we need to calculate the probability of him drawing a $5 token from the cup (1/3) and a $10 token from his pocket (2/3) and then multiply these probabilities to get the total probability (2/9).
Step-by-step explanation:
The probability that Bob will draw $15 in tokens consists of two steps: drawing from the coin cup and then drawing from his pocket. We must calculate the probability for each stage and, finally, multiply these probabilities together to get the total probability of drawing $15.
From the cup, Bob can draw either a $1 token or a $5 token. To get a total of $15, Bob would need to draw a $5 token from the cup, since the highest value in his pocket is $25 and 1+25 is greater than 15. There are two $5 tokens in the cup among six tokens in total, so the probability of drawing a $5 token is 2/6 or 1/3.
Having drawn a $5 token, he now needs to draw a $10 token from his pocket to reach the total of $15. In his pocket, he has two $10 tokens and one $25 token, making three tokens in total. The probability of drawing a $10 token is therefore 2/3.
By multiplying these probabilities, we get the total probability of drawing $15 in tokens: (1/3) * (2/3) = 2/9.
Therefore, the probability that Bob will draw $15 in tokens is 2/9.