4400 Higher June 2009 Paper 3 Q4
4 A bag contains 10 coloured beads.
Ella is going to take at random a bead from the bag.
She says, “The probability that I will take a red bead is 0.35”
Explain why Ella is wrong.
You must show working to justify your answer.
(2)
| Scheme | Marks |
|---|---|
| Examples of complete, correct explanations (i) \(10 \times 0.35\) or 3.5 seen (may be in \(\frac{3.5}{10}\)) AND can’t have half beads or there must be a whole number of (red) beads (ii) \(3\frac{1}{2}\) red beads is impossible (iii) \(\frac{7}{20}\) AND there are (only) 10 beads or you need 20 beads (iv) The probability of any bead/a red bead must be tenths or must have 1 decimal place (v) Gives at least two examples that the probability of taking a red bead is \(\frac{n}{10}\) where \(2 \leqslant n \leqslant 9\) e.g. states 0.3 and 0.4 | B2 |
| (2) | |
| (2 marks) |
Notes
B2: for a complete, correct explanation
B1 for a partially correct explanation
Examples of partially correct explanations
(i) \(\frac{1}{10}\) or 0.1 seen
(ii) Gives one example that the probability of taking a red bead is \(\frac{n}{10}\) where \(2 \leqslant n \leqslant 9\)
(iii) There would be 3.5 red beads.
(iv) You can’t have half beads
(v) \(10 \times 0.35 = 3.5\)
(vi) \(0.35 = \frac{7}{20}\)
Treat statements like ‘Don’t know the number of red beads’ as irrelevant.