(a) Without using Mathematical tables or calculators, simplify: \(3\frac{4}{9} \div (5\frac{1}{3} - 2\frac{3}{4}) + 5\frac{9}{10}\) (b) A number is selected...
Question 1 Report
(a) Without using Mathematical tables or calculators, simplify:
\(3\frac{4}{9} \div (5\frac{1}{3} - 2\frac{3}{4}) + 5\frac{9}{10}\)
(b) A number is selected at random from each of the sets {2, 3, 4} and {1, 3, 5}. Find the probability that the sum of the two numbers is greater than 3 and less than 7.
Answer Details
(a) Brackets first:
\[5\tfrac{1}{3} - 2\tfrac{3}{4} = \tfrac{16}{3} - \tfrac{11}{4} = \tfrac{64 - 33}{12} = \tfrac{31}{12}\] \[3\tfrac{4}{9} \div \tfrac{31}{12} = \tfrac{31}{9} \times \tfrac{12}{31} = \tfrac{12}{9} = \tfrac{4}{3}\] \[\tfrac{4}{3} + 5\tfrac{9}{10} = \tfrac{4}{3} + \tfrac{59}{10} = \tfrac{40 + 177}{30} = \tfrac{217}{30} = 7\tfrac{7}{30}\](b) One number from \(\{2, 3, 4\}\) and one from \(\{1, 3, 5\}\): \(3 \times 3 = 9\) equally likely pairs.
Pairs whose sum satisfies \(3 < \text{sum} < 7\): \((2,3) = 5,\ (3,1) = 4,\ (3,3) = 6,\ (4,1) = 5\), giving 4 outcomes.
\[P = \frac{4}{9}\]Download The App On Google Playstore
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