(a) Use logarithm tables to evaluate (frac{15.05 times sqrt{0.00695}}{6.95 times 10^{2}}).
(b) The first 5 students to arrive in a school on a Monday morning were 2 boys and 3 girls. Of these, two were chosen at random for an assignment. Find the probability that :
(i) both were boys ; (ii) the two were of different sexes.
Explanation
(a) (frac{15.05 times sqrt{0.00695}}{6.95 times 10^{2}})
| No | Log |
| 15.05 | (1.1775 = 1.1775) |
| (sqrt{0.00695}) | (bar{3}.8420 div 2 = bar{2}.9210) |
| = 0.0985 | |
| (6.95 times 10^{2}) | – 2.8420 |
| Antilog = 0.001805 | = (bar{3}.2565) |
(therefore frac{15.05 times sqrt{0.00695}}{6.95 times 10^{2}} approxeq 0.00181) (3 sig. figs)
(b) No of boys = 2, No of girls = 3
(therefore) Total students = 5
(i) P(both are boys) = (frac{2}{5} times frac{1}{4} = frac{1}{10})
(ii) P(both are of different sexes) = P(first a boy, then a girl) or P(first a girl, then a boy)
= (frac{2}{5} times frac{3}{4} + frac{3}{5} times frac{2}{4} )
= (frac{6}{20} + frac{6}{20})
= (frac{12}{20} = frac{3}{5})