2026-09-10T00:15:21.431946 image/svg+xml Matplotlib v3.10.9, https://matplotlib.org/ © EAGLE BEACON GLOBAL Work out the number of red counters in a bag. The...
Question 1 Report
Work out the number of red counters in a bag. The bag holds \(n\) red counters and \(6\) blue counters. The probability of taking a red counter at random is \(\dfrac{2}{5}\).
(a) Work out the value of \(n\).
(b) Two counters are then taken at random without replacement, as shown on the tree diagram. Work out the probability that both are blue.
Answer Details
- (a) If there are \(n\) red and 6 blue counters, there are \(n+6\) counters altogether. The probability of red gives \[\frac{n}{n+6}=\frac{2}{5}.\] Cross-multiplying gives \[5n=2(n+6)=2n+12,\] so \[3n=12\quad\Rightarrow\quad n=4.\] Thus there are 4 red counters. [2 marks]
- (b) The bag now contains \(4+6=10\) counters. For two blue counters without replacement, the first probability is \(\frac{6}{10}\). After a blue counter is taken, only 5 blue counters remain from 9 counters: \[P(\text{both blue})=\frac{6}{10}\times\frac{5}{9}=\frac{30}{90}=\frac{1}{3}.\] [2 marks]
Without replacement is important: the second denominator decreases from 10 to 9.
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