(i)

\begin{align*} \text{P(Number on card is even)} & = {5 \over 11} \end{align*}

(ii) A prime number only has two factors, 1 and itself

\begin{align*} \text{P(Number on card is prime)} & = {4 \over 11} \end{align*}

(iii)

\begin{align*} \text{P(Number on card is even or prime)} & = {5 + 4 \over 11} \\ & = {9 \over 11} \end{align*}

(iv)

\begin{align*} \text{P(Number on card is divisible by 3)} & = {4 \over 11} \end{align*}

(v)

\begin{align*} \text{P(Number on card is neither even nor prime)} & = 1 - \text{P(Number on card is even or prime)} \\ & = 1 - {9 \over 11} \\ & = {2 \over 11} \end{align*}

(i)

\begin{align*} \text{P(Red marble selected)} & = {7 \over 15} \end{align*}

(ii)

\begin{align*} \text{P(Green marble selected)} & = {5 \over 15} \\ & = {1 \over 3} \end{align*}

(iii)

\begin{align*} \text{P(Red or green marble selected)} & = {7 + 5 \over 15} \\ & = {4 \over 5} \end{align*}

(iv)

\begin{align*} \text{P(Neither red nor green marble selected)} & = 1 - \text{P(Red or green marble selected)} \\ & = 1 - {4 \over 5} \\ & = {1 \over 5} \end{align*}

Letter count:

(i)

\begin{align*} \text{P(Pick letter 'U')} & = {3 \over 17} \end{align*}

(ii)

\begin{align*} \text{P(Pick letter 'E')} & = {2 \over 17} \end{align*}

(iii)

\begin{align*} \text{P(Pick letter 'U' or 'E')} & = {3 + 2 \over 17} \\ & = {5 \over 17} \end{align*}

(iv) Consonants are the 'non-vowels' (letters except A E I O U)

\begin{align*} \text{P(Pick consonant)} & = 1 - \text{P(Pick vowel)} \\ & = 1 - {3 + 1 + 2 + 1 \over 17} \\ & = {10 \over 17} \end{align*}

(v)

\begin{align*} \text{P(Pick letter 'U' or consonant)} & = {3 \over 17} + {10 \over 17} \\ & = {13 \over 17} \end{align*}

(vi)

\begin{align*} \text{P(Pick letter 'U' or 'E' or 'L')} & = {3 \over 17} + {2 \over 17} + {3 \over 17} \\ & = {8 \over 17} \end{align*}

(i)

\begin{align*} \text{P(Team win or lose a particular match)} & = {7 \over 10} + {2 \over 15} \\ & = {5 \over 6} \end{align*}

(ii)

\begin{align*} \text{P(Team neither wins nor lose a particular match)} & = 1 - \text{P(Team win or lose a particular match)} \\ & = 1 - {5 \over 6} \\ & = {1 \over 6} \end{align*}

There are 4 suits in a pack of cards (diamond, club, heart, spade).

In each suit, there are 9 number cards (2-10), 1 Ace card and 3 picture cards (K, Q, J)

(i)

\begin{align*} \text{P(Draw a king or a jack)} & = {4 \times 2 \over 52} \\ & = {2 \over 13} \end{align*}

(ii) Prime numbers within 2-10 are 2, 3, 5 and 7

\begin{align*} \text{P(Draw a queen or a card bearing a prime number)} & = {4(1 + 4) \over 52} \\ & = {5 \over 13} \end{align*}

(iii)

\begin{align*} \text{P(Draw a card bearing a number divisible by 3 or by 5)} & = {4(3 + 2) \over 52} \\ & = {5 \over 13} \end{align*}

(iv)

\begin{align*} \text{P(Draw neither a king nor a jack)} & = 1 - \text{P(Draw a king or a jack)} \\ & = 1 - {2 \over 13} \\ & = {11 \over 13} \end{align*}

(i)

\begin{align*} \text{P(He will take 4 or 5 strokes)} & = {1 \over 14 } + {2 \over 7} \\ & = {5 \over 14} \end{align*}

(ii)

\begin{align*} \text{P(He will take 4, 5 or 6 strokes)} & = {1 \over 14 } + {2 \over 7} + {3 \over 7} \\ & = {11 \over 14} \end{align*}

(iii)

\begin{align*} \text{P(He will take more than 6 strokes)} & = 1 - \text{P(He will take 4, 5 or 6 strokes)} \\ & = 1 - {11 \over 14} \\ & = {3 \over 14} \end{align*}

(i)

\begin{align*} \text{P(Alpha or Gamma will win)} & = {4 \over 15} + {1 \over 5} \\ & = {7 \over 15} \end{align*}

(ii)

\begin{align*} \text{P(Alpha, Beta or Gamma will win)} & = {4 \over 15} + {1 \over 10} + {1 \over 5} \\ & = {17 \over 30} \end{align*}

(iii)

\begin{align*} \text{P(Neither Alpha nor Gamma will win)} & = 1 - \text{P(Alpha or Gamma will win)} \\ & = 1 - {7 \over 15} \\ & = {8 \over 15} \end{align*}

(iv)

\begin{align*} \text{P(None of three teams will win)} & = 1 - \text{P(Alpha, Beta or Gamma will win)} \\ & = 1 - {17 \over 30} \\ & = {13 \over 30} \end{align*}

(i)

\begin{align*} \text{P(Priya, Rui Feng or Amirah will win)} & = {1 \over 3} + {1 \over 8} + {1 \over 20} \\ & = {61 \over 120} \end{align*}

(ii)

\begin{align*} \text{P(None of them will win)} & = 1 - \text{P(Priya, Rui Feng or Amirah will win)} \\ & = 1 - {61 \over 120} \\ & = {59 \over 120} \end{align*}

(iii)

\begin{align*} \text{P(Neither Priya nor Rui Feng will win)} & = \text{P(Amirah or other students win)} \\ & = {1 \over 20} + {59 \over 120} \\ & = {13 \over 24} \end{align*}

(a)

(b)(i)

$$ \text{Mutually exclusive. If 3 heads are obtained, there will be no tails} $$

(b)(ii)

$$ \text{Not mutually exclusive. One possible outcome is T H T} $$

(b)(iii)

$$ \text{Not mutually exclusive. Possible outcomes are H T T, T H T and T T H} $$

(b)(iv)

$$ \text{Mutually exclusive} $$

(b)(v)

$$ \text{Not mutually exclusive. One possible outcome is T H T} $$

(b)(vi)

$$ \text{Mutually exclusive} $$

(a)

(b)

$$ \text{Not mutually exclusive. One possible outcome is Miss, Score} $$