Two events $A$ and $B$ are such that $\mathrm{P}(A) = 3p$, $\mathrm{P}(B) = p$, \(\math

Question

Two events $A$ and $B$ are such that $\mathrm{P}(A) = 3p$, $\mathrm{P}(B) = p$, $\mathrm{P}(A|B) = 0.4$ and $\mathrm{P}(A \cup B) = 0.9$. Find the value of $p$.[3] Explain what is meant by $\mathrm{P}(A' \cap B')$ and find its value.[2] Explain whether the events $A$ and $B$ are independent.[1] Complete the Venn diagram to show the probability in each of the four regions.[1]

Accepted Answer

(a)p=0.25 (b)0.1

2024 NYJC H1 Q8

2024 NYJC H1 Q8