**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(A**

_{T}

**) = 60/100 & P(A**

_{C}

**) = 40/100**

**P(B**_{T}**) = 90/100 & P(B**_{C}**) = 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!