IB Math SL – Probability

IB Math SL – Probability

Questions and Answers

1. Probability – IB Mathematics SL – IB maths SL

How can we find the probability P(A \cap B') if A and B are two events such that P(A)=0.6, P(B)=0.2 and P(A \cup B)=0.7?

Solution

Probability – IB Mathematics SL – IB Maths SL

We know that P(A \cup B)=P(A)+P(B)-P(A \cap B) \Rightarrow

P(A \cap B)=0.6+0.2-0.7=0.1

Finally, we have P(A \cap B')=P(A)-P(A \cap B) =0.6-0.1=0.5

2. Conditional Probability question – IB Mathematics SL – IB maths SL

How can we calculate the probability P(A/B') if A and B are two events such that P(A)=0.5, P(B)=0.4 and P(A/B)=0.8?

Solution

Conditional Probability question – IB Mathematics SL – IB maths SL

From conditional probability formula, we have that

P(A/B)=\frac{P(A \cap B)}{P(B)}\Rightarrow

0.8=\frac{P(A \cap B)}{0.4} \Rightarrow P(A \cap B) =0.8 \cdot 0.4=0.32

Finally, we have that P(A/B')=\frac{P(A \cap B')}{P(B')}= \frac{P(A)- P(A \cap B)}{1-P(B)}=

=\frac{0.5-0.32}{1-0.4}=\frac{0.18}{0.6}=0.3