WAEC 2018 · Paper 2 · Q12

Statistics & correlation
Probability & distributions

Number of heads	0	1	2	3	4	5	6	7	8	9	10
Frequency	2	7	23	36	11	61	100	12	8	5	3

Ten coins were tossed together a number of times. The distribution of the number of heads obtained is given in the table. Calculate, correct to three decimal places, the:

(a)
mean number of heads;
(b)
probability of getting an even number of heads;
(c)
probability of getting an odd number of heads.

Worked solution (try it first)

(a)

$\sum f = 268$ and $\sum fx = 1333$ , so the mean is $\dfrac{1333}{268} \approx 4.974$ .

(b)

Even numbers of heads are 0, 2, 4, 6, 8 and 10: $2 + 23 + 11 + 100 + 8 + 3 = 147$ , so $P = \dfrac{147}{268} \approx 0.549$ .

(c)

Odd: $7 + 36 + 61 + 12 + 5 = 121$ , so $P = \dfrac{121}{268} \approx 0.451$ .

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