Question

Bill has some counter in a bag.

3 of the counters are red
7 of the counters are blue
the rest of the countes are yellow
Bill takes at random a counter from the bag
The probability that he takes a yellow counter is 2/7
(b) How many yellow counters are in the bag before Bill takes a counter

Answer 1

9514 1404 393

Answer:

4

Explanation:

The 10 non-yellow counters in the bag represent 5/7 of the total number of counters, c.

10 = (5/7)c

10(7/5) = c = 14

There are 14 counters in the bag, of which 14-10 = 4 are yellow.

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Alternate solution

Let y represent the number of yellow counters in the bag. The probability of drawing a yellow counter is the number of yellow counters divided by the total number of counters:

y/(y +3 +7) = 2/7

Multiply both sides of this equation by 7(y+10) to get ...

7y = 2(y +10)

7y = 2y +20 . . . . eliminate parentheses

5y = 20 . . . . . . . . subtract 2y

y = 20/5 = 4 . . . . divide by the coefficient of y

There are 4 yellow counters in the bag before any are taken.

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Another alternate solution

If the probability of yellow is 2/7, the ratio of yellow (y) to non-yellow is ...

yellow : non-yellow = 2 : (7-2) = 2 : 5 = y : (3+7) = y : 10 = 4 : 10

⇒ y = 4

There are 4 yellow counters in the bag.