(a) P and Q are points on the parallel of latitude 68.7°S, their longitudes being 124°W and 56°E respectively. What is their distance apart measured along t...
Question 1 Report
(a) P and Q are points on the parallel of latitude 68.7°S, their longitudes being 124°W and 56°E respectively. What is their distance apart measured along the parallel of latitude? [Take R = 6400km, \(\pi = 3.142\)]. (Give your answers to 3 significant figures).
(b) A bag contains four red, three white and five green balls. (i) If one ball is picked at random, what is the probability that it is not green? (ii) if two balls are picked at random without replacement, what is the probability that one is red and the other white?
Answer Details
(a) P and Q lie on the parallel \(68.7^\circ\)S, with longitudes \(124^\circ\)W and \(56^\circ\)E. The longitude difference is
\[ 124^\circ + 56^\circ = 180^\circ. \]The radius of the parallel of latitude is \(R\cos 68.7^\circ\), so the distance along the parallel is
\[ \frac{180}{360} \times 2\pi R \cos 68.7^\circ = \frac{1}{2}\times 2 \times 3.142 \times 6400 \times \cos 68.7^\circ. \]With \(\cos 68.7^\circ = 0.3633\):
\[ = 3.142 \times 6400 \times 0.3633 = 7304\ \text{km} \approx 7300\ \text{km (3 s.f.).} \](b) Bag: 4 red, 3 white, 5 green, total 12.
(i) \(P(\text{not green}) = 1 - P(\text{green}) = 1 - \dfrac{5}{12} = \dfrac{7}{12}.\)
(ii) Two balls without replacement, one red and one white (red-then-white or white-then-red):
\[ \frac{4}{12}\times\frac{3}{11} + \frac{3}{12}\times\frac{4}{11} = \frac{12}{132} + \frac{12}{132} = \frac{24}{132} = \frac{2}{11}. \]Download The App On Google Playstore
Everything you need to excel in your exams
