.
Question 1
The 112 students sat for an examination.
Question 1 was answered by 50 students, Question 2 by 66 students, Question 3 by 38 students.
32 students attempeted Q2 and Q1, 22 students attempted Q2 and Q3, 20 students attempted Q3 Q1,
8 students attempted all the questions. How many students didn't attempt any questi
Question 2
Supposed 2 coins are tosed,events A and B are defined as follows; A is the event of getting a head in the first coin.
B is the event that the coin falls alike.Fknd the probability of the event A happening given that B has happened
and the probability of event B happening given that A has already happened.
Question 3
Past records shown that the probability of a school football twam winning a match is 0.7.
How many possible games might the school win in 30 matches
~~~~~~~~~~~~~~~~~~~
I will answer Q1 and Q3, only.
Question 1
Use the Inclusion-Exclusion principle (formula). The number of those who attempted at least one of the questions is
n(Q1 U Q2 U Q3) = n(Q1) + n(Q2) + n(Q3) - n(Q1 and Q2) - n(Q1 and Q3) - n(Q2 and Q3) + n(Q1 and Q2 and Q3) =
= 50 + 66 + 38 - 32 - 20 - 22 + 8 = 88.
Thus the number of those who didn't attempt any question is the COPMPLEMENT of 88 to 112, i.e. 112 - 88 = 24. ANSWER
Question 3
They ask about the mathematical expectation. You may use your intuition (= common sense) or strict mathematical formula
for the mathematical expectation of the binomial distribution with 30 trials and the probability of success p = 0.7
for each individual trial.
In any case, the ANSWER is this number E = n*p = 0.7*30 = 21.
Solved.
------------------
On inclusion-exclusion principle, see this Wikipedia article
https://en.wikipedia.org/wiki/Inclusion%E2%80%93exclusion_principle
To see many other similar (and different) solved problems on Inclusion-Exclusion, see the lessons
- Counting elements in sub-sets of a given finite set
- Advanced problems on counting elements in sub-sets of a given finite set
- Challenging problems on counting elements in subsets of a given finite set
- Selected problems on counting elements in subsets of a given finite set
- Inclusion-Exclusion principle problems
in this site.
Happy learning (!)