WAEC 2016 · Paper 2 · Q4

Probability

Score	1	2	3	4	5	6
Frequency	25	30	$x$	28	40	32

The table shows the outcome when a die is thrown a number of times. If the probability of obtaining a 3 is 0.225:

(a)
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.

Worked solution (try it first)

(a)

The total number of throws is $25 + 30 + x + 28 + 40 + 32 = 155 + x$ .
So $P(3) = \frac{x}{155 + x} = 0.225$ .
Then $x = 0.225(155 + x) = 34.875 + 0.225x$ , so $0.775x = 34.875$ and $x = 45$ .
The die was thrown $155 + 45 = 200$ times.

(b)

Even scores: 2, 4, 6.
Prime scores: 2, 3, 5.
Even or prime: 2, 3, 4, 5, 6, with 2 counted only once.
(1 is neither even nor prime.)
These happened $30 + 45 + 28 + 40 + 32 = 175$ times, so the probability is $\frac{175}{200} = \frac78$ .

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