Question 2 - A-Level Maths

Exam Board	Edexcel
Module	S2 (Statistics 2)
Year	2023
Session	January
Topic	Binomial Distribution
Type	Probability distribution table

A bag contains a large number of coins. It only contains 20 p and 50 p coins. A random sample of 3 coins is taken from the bag.
1. List all the possible combinations of 3 coins that might be taken.
Let \(\bar { X }\) represent the mean value of the 3 coins taken.
Part of the sampling distribution of \(\bar { X }\) is given below.
\(\bar { x }\) 20 \(a\) \(b\) 50
\(\mathrm { P } ( \bar { X } = \bar { x } )\) \(\frac { 4913 } { 8000 }\) \(c\) \(d\) \(\frac { 27 } { 8000 }\)
Write down the value of \(a\) and the value of \(b\) The probability of taking a 20p coin at random from the bag is \(p\) The probability of taking a 50p coin at random from the bag is \(q\)
Find the value of \(p\) and the value of \(q\)
Hence, find the value of \(c\) and the value of \(d\) Let \(M\) represent the mode of the 3 coins taken at random from the bag.
Find the sampling distribution of \(M\)

\(\bar { x }\)	20	\(a\)	\(b\)	50
\(\mathrm { P } ( \bar { X } = \bar { x } )\)	\(\frac { 4913 } { 8000 }\)	\(c\)	\(d\)	\(\frac { 27 } { 8000 }\)