a. A pack of 52 playing cards is 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 150º, and the bearing of R from Q is 060º. If |PQ| = 5 m and |QR| = 3 m, find the bearing of R from P, correct to the nearest degree.
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)
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