Ten coins were tossed together a number of times. The distribution of the number of heads obtained is given in the following table :
| No 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 |
Calculate, correct to three decimal places, the :
(a) mean number of heads ;
(b) probability of getting an even head ;
(c) probability of getting an odd number.
Explanation
| No of heads | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | Total |
| Frequency | 2 | 7 | 23 | 36 | 11 | 61 | 100 | 12 | 8 | 5 | 3 | 268 |
| \(fx\) | 0 | 7 | 46 | 108 | 44 | 305 | 600 | 84 | 64 | 45 | 30 | 1333 |
(a) Mean \(\bar{x} = \frac{\sum fx}{\sum f}\)
= \(\frac{1333}{268}\)
= \(4.974\) (to 3 d.p.)
(b) Even numbers = 147
p(even number) = \(\frac{147}{268}\)
= \(0.5485 \approxeq 0.549\)
(c) Odd numbers = 121
p(odd number) = \(\frac{121}{268}\)
= \(0.4515 \approxeq 0.452\)