Review practice · Section 1 of 3

Events A and B are such that $P(A)=k+\frac16$, $P(B)=k+\frac1{12}$ and $P(A\cup B)=\frac12$.

Given A and B are independent, find the value of k.3 marks

$P(A)=0.7$, $P(B\mid A')=0.4$ and $P(A\cap B)=0.28$.

(i) Determine, with a reason, whether A and B are independent.2 marks

(ii) Find $P[(A\cap B)\mid(A\cup B)]$.3 marks

$P(X\mid Y)=1/2$, $P(Y\mid X)=2/3$ and $P(X\cup Y)=5/6$. Find

(i) $P(X)$,3 marks

(ii) $P(X\cup Y')$.2 marks

$P(A)=3/5$, $P(B)=3/4$ and $P(A\mid B')=1/2$.

(i) Find $P(A\cap B)$.2 marks

(ii) Find $P(A'\mid A\cup B)$.3 marks

A third event C has $P(C)=1/2$ and is independent of A.

(iii) Find $P(A'\cap C)$.1 mark

(iv) Hence show that $3/40\le P(A'\cap B\cap C)\le1/5$.2 marks

A and B are independent events, with $P(A\cup B)=3/4$ and $P(A'\cap B)=2/15$. Find

(i) $P(A)$,

(ii) $P(B)$.

Two fair dice, one white and one red, are thrown. Event A is that the white score is prime; event B is that the sum of the scores is 9.

(i) Find $P(A\mid B)$ and hence determine whether A and B are independent.3 marks

(ii) Event C is that the red score is a perfect square. Find $P(B'\cap C')$.2 marks