Theory question 104
Probability(a) A pack of 52 playing cards in shuffled and a card is drawn at random. Calculate the probability that it is either a five or a red nine. [Hint: There are 4 fives and 2 red nines in a pack of 52 cards].
(b) P, Q and R are points in the same horizontal plane. The bearing of Q from P is 150° and the bearing of R from Q is 060°. If |PQ| = 5cm and |QR| = 3m, find the bearing of R from P, correct to the nearest degree.
Show the model answer
Model answer
(a) P(five or red nine) = 4/52 + 2/52 = 6/52 = 3/26
(b) Sketch: the bearing of P from Q is 330°, so ∠PQR = 360° − 330° + 60° = 90°
tan ∠QPR = 3/5 = 0.6, so ∠QPR ≈ 31°
R lies to the east side of PQ, so the bearing of R from P = 150° − 31° = 119°
Explanation
Find the angle at Q from the back bearing first; it is a right angle here.