(a)
Difference in longitudes = 124° + 56° = 180°
Distance PQ = \(\frac{180°}{360°} \times 2\pi r\)
where \(r = R \cos \theta\)
\(/PQ/ = \frac{180}{360} \times 2 \times 3.142 \times R \cos 68.7°\)
\(/PQ/ = 3.142 \times 6400 \times 0.3633\)
= \(7305.53 km\)
\(\approxeq 7300 km\) (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)
= \(\frac{4}{12} \times \frac{3}{11} + \frac{3}{12} \times \frac{4}{11}\)
= \(\frac{2}{11}\)