a. Total number of cards = 52 There are 4 fives and 2 red nines A card is drawn at random Pr(Either a five or a red nine) = Pr(five) + Pr(red nine) = \(\frac{4}{52}\) + \(\frac{2}{52}\) = \(\frac{6}{52}\) = \(\frac{3}{26}\) b. see diagram above ∠Q = 90° Δ PQR is a right-angled triangle. PR\(^2\) = PQ\(^2\) + QR\(^2\) PR\(^2\) = 5\(^2\) + 3\(^2\) = 25 + 9 PR\(^2\) = 34 = > PR = \(\sqrt{34}\) = 5.831 Let angle P = θ Therefore, \(\frac{5.831}{sin 90°}\) = \(\frac{3}{sin θ}\) 5.831 sin θ = 3 Therefore, Sin θ = \(\frac{3}{5.831}\) = 0.5145 \(\theta\) = Sin\(^{-1}\)(0.5145) = 30.96º Bearing of R from P = 150° - θ = 150° - 30.96° = 119° (to the nearest degree)