IB Mathematics Analysis and Approaches Question Type 1: Finding the Value of Certain Probability Events Given the Values of Others Exercises

Events $A$ and $B$ partition the sample space with $P(A)=0.4$, $P(B)=0.6$. Given $P(C\mid A)=0.3$ and $P(C\mid B)=0.5$, find $P(A\mid C)$.

If $A$, $B$, and $C$ are independent with $P(A)=0.2$, $P(B)=0.5$, and $P(C)=0.3$, find $P(A\mid B\cap C^{\prime })$.

Given $P(A)=0.3$, $P(B)=0.6$, and $P(B\mid A)=0.2$, find $P(A\mid B^{\prime })$.

Given $P(A)=0.4$, $P(B)=0.3$, and $P(A\mid B^{\prime })=0.5$, find $P(B\mid A)$.

Given $P(A)=0.4$, $P(B)=0.5$, and $P(A\cap B)=0.2$, find $P(B\mid A^{\prime })$.

Events $A$, $B$, and $C$ are mutually exclusive and exhaustive with $P(A)=0.25$, $P(B)=0.35$, and $P(C)=0.40$. Given $P(D\mid A)=0.2$, $P(D\mid B)=0.5$, and $P(D\mid C)=0.3$, find $P(B\mid D)$.

If $A$ and $B$ are independent with $P(A)=0.45$ and $P(B)=0.6$, find $P(A\mid B^{\prime })$.

Given $P(A)=0.4$, $P(B)=0.5$, $P(C)=0.3$, $P(A\cap B)=0.2$, $P(B\cap C)=0.1$, $P(A\cap C)=0.12$, and $P(A\cap B\cap C)=0.05$, find $P(C\mid A\cup B)$.

Given $P(A)=0.7$, $P(B)=0.5$, and $P(A\cap B)=0.35$, find $P(A^{\prime }\mid B^{\prime })$.

Given $P(A)=0.25$, $P(B)=0.5$, and $P(A\mid B)=0.4$, find $P(A\cap B^{\prime })$.

Given $P(A)=0.35$, $P(B)=0.55$, and $P(A\cup B)=0.75$, find $P(B\mid A^{\prime })$.

If $A$ and $B$ are independent with $P(A)=0.6$ and $P(B)=0.7$, find $P(A\mid B^{\prime })$.