Question

4(a) [Table: Scores 1,2,3,4,5,6; Frequency 25,30,x,28,40,32] The table above shows the outcome when a die is thrown a number of times. If the probability of obtaining a 3 is 0.225; How many times was the die thrown?
(b) Calculate the probability that a trial chosen at random gives a score of an even number or a prime number.

Accepted Answer

(a) Let N = total number of times the die was thrown.
P(3) = x/N = 0.225
Also, N = 25+30+x+28+40+32 = 155+x
x = 0.225N = 0.225(155+x)
x = 34.875+0.225x
0.775x = 34.875
x = 45
N = 155+45 = 200
The die was thrown 200 times.

(b) x=45, so frequencies: 25,30,45,28,40,32 (total 200)
Even numbers: scores 2,4,6 → frequencies 30+28+32=90
Prime numbers: scores 2,3,5 → frequencies 30+45+40=115
Even or Prime (union, 2 counted once) = 25(scores 1)... 
Numbers that are even or prime: {2,3,4,5,6} (all except 1) → frequency = 30+45+28+40+32=175
P(even or prime) = 175/200 = 7/8

WAEC Mathematics 2016 Theory — Question 4

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