Question

The probability of selecting a blue marble and a red marble from a bag containing red, blue and green marbles is `1/3` and `1/5` respectively. If the bag contains 14 green marbles, then find:

1. number of red marbles. 
2. total number of marbles in the bag.

Answer 1

Given:

Let r = number of red marbles, b = number of blue marbles, g = number of green marbles = 14.

P(blue) = `b/n = 1/3` and P(red) = `r/n = 1/5`, where n = total number of marbles.

Step-wise calculation:

1. From probabilities:

`b = n/3`

`r = n/5`

2. Total count:

n = r + b + g

= `n/5 + n/3 + 14`

3. Combine fractions:

`n - (n/5 + n/3) = 14`

`n/5 + n/3 = (3n + 5n)/15`

= `(8n)/15`

`(n - 8n)/15 = (7n)/15`

`(7n)/15 = 14`

4. Solve for n:

`n = 14 xx 15/7`

= 2 × 15

= 30

5. Find r:

`r = n/5`

= `30/5`

= 6