(a) P and Q are points on the parallel of latitude 68.7^\circS, their longitudes being 124^\circW and 56^\circE 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?
Verified Correct Answer: .
Step-by-Step Mathematical Solution
(a)
Difference in longitudes = 124^\circ + 56^\circ = 180^\circ
Distance PQ = \(\frac{180^\circ}{360^\circ} \times 2\pi r\)
where \(r = R \cos \theta\)
\(/PQ/ = \frac{180}{360} \times 2 \times 3.142 \times R \cos 68.7^\circ\)
\(/PQ/ = 3.142 \times 6400 \times 0.3633\)
= \(7305.53 km\)
\(\approxeq 7300 km\) (3 sig. figs)
(b) Red balls = 4, white = 3 ; green = 5
Total = 4 + 3 + 5 = 12 balls.
(i) P(green) = \(\frac{5}{12}\)
P(not green) = \(1 - \frac{5}{12} = \frac{7}{12}\)
(ii) P(picking red and white) = P( red then white) or P(white then red)
= \(\frac{4}{12} \times \frac{3}{11} + \frac{3}{12} \times \frac{4}{11}\)
= \(\frac{2}{11}\)
Source: Myschool Past Questions Archive (Record #54519)