Ten coins were tossed together a number of…

Question 1 Report

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 ;

Answer

Answer Details

Let \(x\) = number of heads and \(f\) = frequency. First find \(N = \sum f\).

\(x\)	0	1	2	3	4	5	6	7	8	9	10	Total
\(f\)	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 number of heads.

\[ \bar{x} = \frac{\sum fx}{\sum f} = \frac{1333}{268} = \mathbf{4.974} \]

(b) Probability of an even number of heads. Even outcomes are \(x = 0,2,4,6,8,10\) with frequencies \(2+23+11+100+8+3 = 147\).

\[ P(\text{even}) = \frac{147}{268} = \mathbf{0.549} \]

(c) Probability of an odd number of heads. Odd outcomes are \(x = 1,3,5,7,9\) with frequencies \(7+36+61+12+5 = 121\).

\[ P(\text{odd}) = \frac{121}{268} = \mathbf{0.451} \]

Check: \(0.549 + 0.451 = 1.000\).

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...