A test has five questions. To pass the test, at least three of the questions must be answered correctly. The probability that Mark answers a question correctly is \(\frac15\). Let \(X\) be the number of questions that Mark answers correctly. [6] Find \(E(X)\). Find the probability that Mark passes the test. \(y\)\(0\)\(1\)\(2\)\(3\)\(4\)\(5\) \(P(Y=y)\)\(0.67\)\(0.05\)\(a+2b\)\(a-b\)\(2a+b\)\(0.04\) [8] Show that \(4a + 2b = 0.24\). Given that \(E(Y) = 1\), find \(a\) and \(b\). Find which student is more likely to pass the test.[3]

Complete a binomial probability table, solve an unknown success probability and calculate a pass probability.

17 marks

ProbabilityQuestionBank.pdf

A test has five questions. To pass the test, at least three of the questions must be answered correctly. The probability that Mark answers a question correctly is \(\frac15\). Let \(X\) be the number of questions that Mark answers correctly.

[6]
1. Find \(E(X)\).
2. Find the probability that Mark passes the test.
\(y\) \(0\) \(1\) \(2\) \(3\) \(4\) \(5\)
\(P(Y=y)\) \(0.67\) \(0.05\) \(a+2b\) \(a-b\) \(2a+b\) \(0.04\)
[8]
1. Show that \(4a + 2b = 0.24\).
2. Given that \(E(Y) = 1\), find \(a\) and \(b\).
Find which student is more likely to pass the test.[3]

\(y\)	\(0\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)
\(P(Y=y)\)	\(0.67\)	\(0.05\)	\(a+2b\)	\(a-b\)	\(2a+b\)	\(0.04\)

Solution:

Solution locked

Similar questions are unavailable for this question.

Answer:Bill passes with probability \((a-b)+(2a+b)+0.04=0.19\), so Bill is more likely to pass.

Need help? Join our JC Math tuition classes.

Learn more