IB Math SL – Probability

Questions and Answers

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 $P(A \cap B')=P(A)-P(A \cap B) =0.6-0.1=0.5$

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 $P(A/B')=\frac{P(A \cap B')}{P(B')}= \frac{P(A)- P(A \cap B)}{1-P(B)}=$

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