For events $A$ and $B$, it is given that ${P(A) = \frac{1}{4}}$ and ${P(B) = \frac{1}{2}}$. Given th

Question

For events $A$ and $B$, it is given that ${P(A) = \frac{1}{4}}$ and ${P(B) = \frac{1}{2}}$. Given that ${P(A'|B) = \frac{3}{4}}$, determine whether events $A$ and $B$ are independent and calculate ${P(A \cup B)}$. [3] For a third event $C$, it is given that ${P(C|A) = \frac{2}{3}}$. Find the value of ${P(A \cap C)}$. [2] Find the number of ways in which the word EVERYDAY can be arranged if all the vowels (A, E) must be together and the two ‘Y’s must be separated. [3] the repeated letters E and Y must appear symmetrical about the centre of the word (e.g. EVRYYDAE, YVERDEAY). [2]

Accepted Answer

(a)(i) Independent, $P(A\cup B)=\dfrac58$ (a)(ii) $P(A\cap C)=\dfrac16$ (b)(i) $720$ (b)(ii) $288$

2016 MJC P2 Q9

2016 MJC P2 Q9

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