IBDP Mathematics Question Analysis Topic: Mathematics - Probability
Exam Questions:
1) A speaks truth in 60% of the cases, while B in 90% of the cases. In what percent of cases are thy likely to contradict each other in stating the same fact? In the cases of contradiction do you think, the statement of B will carry more weight as he speaks truth in more number of cases then A?
2) P speaks truth in 70% of the cases and Q in 30% of the cases. In what per cent of cases are they likely to agree in stating the same fact?
Do you think, when they agree, means both are speaking truth?
Answers:
For IBDP Mathematics, you should know:
1) Let's define a few variables first.
T = Truth and C = Contradiction.
We have a few givens:
P(AT) = 60/100 & P(AC) = 40/100
P(BT) = 90/100 & P(BC) = 10/100
P(contradiction) = 60/100 x 10/100 + 40/100 x 90/100
= 600/10000 + 3600/10000 = 600+3600/10000?
= 4200/10000 = 42%
Ultimately, in cases of contradiction, the statements of B would infact carry more weight.
2) Let's define some variables, first.
A = Event that A speaks the truth & B = Event that B does.
So, P(A) = 70/100 = 7/10
P(B) = 30/100 = 3/10
P(A - lie) = 1 - 7/10 = 3/10
P(B - lie) = 1 - 3/10 = 7/10
Now,
A and B contradicting each other = [A lies and B is true] or [B is true and B lies]
= P(A) x P(B - lie) + P(A - lie) x P(B)
= 7/10 x 7/10 + 3/10 x 3/10 = 29/20
= 29/50 x 100 = 58%
Work hard for your IBDP Mathematics examination!
End of analysis. Great!