CAIE S1 2019 June — Question 2 3 marks

Exam BoardCAIE
ModuleS1 (Statistics 1)
Year2019
SessionJune
Marks3
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicIndependent Events
TypeFind parameter using independence
DifficultyModerate -0.8 This is a straightforward application of the multiplication rule for independent events with basic probability fractions. Students set up P(plum from Jameel) × P(plum from Rosa) = 1/4, giving (5/8) × (x/(x+6)) = 1/4, then solve the simple linear equation. Requires only routine probability calculation and basic algebra, making it easier than average.
Spec2.03a Mutually exclusive and independent events

2 Jameel has 5 plums and 3 apricots in a box. Rosa has \(x\) plums and 6 apricots in a box. One fruit is chosen at random from Jameel's box and one fruit is chosen at random from Rosa's box. The probability that both fruits chosen are plums is \(\frac { 1 } { 4 }\). Write down an equation in \(x\) and hence find \(x\). [3]

Question 2:
AnswerMarks Guidance
AnswerMarks Guidance
Jameel: \(P(\text{plum}) = \dfrac{5}{8}\), Rosa: \(P(\text{plum}) = \dfrac{x}{x+6}\)M1 *Their* 2 probabilities for \(P(\text{plum})\) multiplied and equated to \(\frac{1}{4}\)
\(\dfrac{5}{8} \times \dfrac{x}{x+6} = \dfrac{1}{4}\)A1 Correct equation oe
\((x =) 4\)A1 SC correct answer with no appropriate equations i.e. common sense B1
## Question 2:

| Answer | Marks | Guidance |
|--------|-------|----------|
| Jameel: $P(\text{plum}) = \dfrac{5}{8}$, Rosa: $P(\text{plum}) = \dfrac{x}{x+6}$ | **M1** | *Their* 2 probabilities for $P(\text{plum})$ multiplied and equated to $\frac{1}{4}$ |
| $\dfrac{5}{8} \times \dfrac{x}{x+6} = \dfrac{1}{4}$ | **A1** | Correct equation oe |
| $(x =) 4$ | **A1** | **SC** correct answer with no appropriate equations i.e. common sense **B1** |
2 Jameel has 5 plums and 3 apricots in a box. Rosa has $x$ plums and 6 apricots in a box. One fruit is chosen at random from Jameel's box and one fruit is chosen at random from Rosa's box. The probability that both fruits chosen are plums is $\frac { 1 } { 4 }$. Write down an equation in $x$ and hence find $x$. [3]\\

\hfill \mbox{\textit{CAIE S1 2019 Q2 [3]}}