Question

In a tin there are only blue counters, white counters and red counters. There are 5 blue counters. When one is chosen at random, P(blue)=1/8 and P(white)=3/5. How many red counters are in the tin?

Answer 1

To find the number of red counters in the tin, calculate the total number of counters using the probability of drawing a blue counter, then subtract the number of blue and white counters to find the remainder, which are red.

Step-by-step explanation:

The question involves calculating the total number of counters in a tin knowing the probabilities of drawing counters of different colors and the exact number of blue counters. We know that P(blue)=1/8 and there are 5 blue counters. As the probability of drawing a blue counter is 1/8, and there are 5 blue counters, we calculate the total number of counters by multiplying the number of blue counters by 8, as probability is given by the ratio of favorable outcomes (number of blue counters) to total possible outcomes (total number of counters). Therefore, the total number of counters will be 5 x 8 = 40. We also know that P(white)=3/5, thus the number of white counters is 3/5 of the total, which is 3/5 x 40 = 24 white counters. To find the number of red counters, we subtract the number of blue and white counters from the total: 40 – (5 + 24) = 11 red counters.