Department of Electronic Engineering
Royal Holloway University of London
EE1120: Mathematics for Engineers 2 (2021-22)
Problems Class 5
Question 1 (5 marks)
Two candidates are being interviewed for one job. The probability of Candidate A gets hired is 65%, the
probability of candidate B gets hired is 25%. Draw a Venn diagram of the possible outcomes in which
someone gets hired. What is the probability that neither candidate gets hired?
Question 2 (9 marks)
Three candidates are being interviewed for three posts. However, not all of the posts need to be filled.
The probability of Candidate A getting the job is 75%, the probability of candidate B getting the job is 20%,
the probability of candidate C getting the job is 50%.
i.
Draw a Venn diagram of the possible outcomes in which someone gets hired.
What is the probability that
ii.
Candidates A and B both get jobs
iii.
Only Candidate C gets a job
iv.
None of the candidates get a job
Question 3 (2 marks)
The average time between twins being born is 21 mins. Assuming that the time of the first birth is entirely
random, what is the probability that a set of twins have different birthdays?
Question 4 (15 marks)
A boardgame uses a twelve-sided die. Unfortunately, the twelve-sided die has been lost. Your friend
suggests that instead of the 12-sided die, you could roll two normal (6-sided) dice instead and add up the
numbers. Use your understanding of statistics to assess whether your friend’s suggestion would affect the
results thrown, comparing the cardinality of the throws and the probability of obtaining each number. Are
there any circumstances where the probability of throwing a particular number is the same using the two
6-sided dice as would have been achieved using the 12-sided die?
Question 5 (12 marks)
The probability of a resistor blowing in a circuit is 1%. Given that one resistor has blown, the probability of
a 2nd resistor blowing is 10%. If 0 resistors blow, the probability of the device failing is 0.01%. If 1 resistor
blows the probability of the device failing is 20%. If 2 resistors blow the probability of the device failing is
50%. What is the probability of the device failing?
Question 6 (7 marks)
A keypad has digits 0-9 and needs 4 button presses to unlock the code.
i.
ii.
iii.
What is the probability of randomly guessing the code if any number can be selected?
If the manufacturer requires a code to consist of four different digits how many
permutations (ordered arrangements) and combinations (non-ordered arrangements) are
possible?
A thief detects which 4 buttons unlock the code, but not what order. How many
permutations do they need to go through to be sure to crack the code?