Question

5(a) A fair die was rolled a certain number of times and the outcomes are as shown in the table below: Number:1,2,3,4,5,6 | No. of times:5,m,55,45,25,40. If the probability of obtaining a 2 was 0.15, find: (a) the value of m; (b) the total number of times the die was rolled; (c) the probability of obtaining an even number.

Accepted Answer

(a) Total outcome = 5+m+55+45+25+40 = 170+m. Since P(obtaining 2)=0.15= (No of times '2' occurred)/(Total outcome) = m/(170+m). Cross multiplying: m=0.15(170+m) => m=25.5+0.15m. Collecting like terms: m-0.15m=25.5 => 0.85m=25.5. Dividing both sides by 0.85: m=30.
(b) Total number of times the die was cast = Total outcome = 170+m = 170+30=200.
(c) P(even numbers) = P(obtain 2)+P(obtain 4)+P(obtain 6) = 30/200 + 45/200 + 40/200 = 115/200 = 23/40.

WAEC Mathematics 2020 Theory — Question 5

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