SPS SPS SM Statistics 2021 May — Question 1 8 marks

Exam BoardSPS
ModuleSPS SM Statistics (SPS SM Statistics)
Year2021
SessionMay
Marks8
TopicTree Diagrams
TypeMulti-stage with stopping condition
DifficultyModerate -0.8 This is a straightforward tree diagram question with clearly defined probabilities (1/10, 1/5, 1/3 for red) and standard conditional probability calculations. Part (d) requires Bayes' theorem but in a routine context. The multi-stage stopping condition adds mild complexity, but all parts follow standard textbook patterns with no novel insight required.
Spec3.03r Friction: concept and vector form3.03t Coefficient of friction: F <= mu*R model3.03u Static equilibrium: on rough surfaces3.03v Motion on rough surface: including inclined planes
  1. Three Bags, \(A , B\) and \(C\), each contain 1 red marble and some green marbles.
\begin{displayquote} Bag \(A\) contains 1 red marble and 9 green marbles only
Bag \(B\) contains 1 red marble and 4 green marbles only
Bag \(C\) contains 1 red marble and 2 green marbles only \end{displayquote} Sasha selects at random one marble from \(\operatorname { Bag } A\).
If he selects a red marble, he stops selecting.
If the marble is green, he continues by selecting at random one marble from Bag \(B\).
If he selects a red marble, he stops selecting.
If the marble is green, he continues by selecting at random one marble from Bag \(C\).
  1. Draw a tree diagram to represent this information.
  2. Find the probability that Sasha selects 3 green marbles.
  3. Find the probability that Sasha selects at least 1 marble of each colour.
  4. Given that Sasha selects a red marble, find the probability that he selects it from Bag \(B\).
\begin{enumerate}
  \item Three Bags, $A , B$ and $C$, each contain 1 red marble and some green marbles.
\end{enumerate}

\begin{displayquote}
Bag $A$ contains 1 red marble and 9 green marbles only\\
Bag $B$ contains 1 red marble and 4 green marbles only\\
Bag $C$ contains 1 red marble and 2 green marbles only
\end{displayquote}

Sasha selects at random one marble from $\operatorname { Bag } A$.\\
If he selects a red marble, he stops selecting.\\
If the marble is green, he continues by selecting at random one marble from Bag $B$.\\
If he selects a red marble, he stops selecting.\\
If the marble is green, he continues by selecting at random one marble from Bag $C$.\\
(a) Draw a tree diagram to represent this information.\\
(b) Find the probability that Sasha selects 3 green marbles.\\
(c) Find the probability that Sasha selects at least 1 marble of each colour.\\
(d) Given that Sasha selects a red marble, find the probability that he selects it from Bag $B$.\\

\hfill \mbox{\textit{SPS SPS SM Statistics 2021 Q1 [8]}}
This paper (6 questions)
View full paper
Q1 8 Q2 8 Q3 6 Q4 8 Q5 8 Q6 7