Question

write the sample space for the experiment of flipping 4 fair coins, one after the other. Find the expected value of the number of heads

Answer 1

(a)

Sample Space for flipping 4 fair coins :

S = { HHHH, HTHH, THHH, HTHT,

       HHHT, HTTH, TTHH, THTH,

        HHTT, HHTH, TTTH,THHT,

        HTTT, TTTT, TTHT, THTT }

Total number of events = 2⁴ = 16

(b)

The Probability Distribution of X = Number of Heads is got as follows:

x	p
0	1/16=0.0625
1	4/16 =0.25
2	6/16 = 0.375
3	4/16=0.25
4	1/16 = 0.0625

     The Expected value of the number of Heads = E(X) is got as ollws::

x	p	x p
0	0.0625	0
1	0.25	0.25
2	0.375	0.75
3	0.25	0.75
4	0.0625	0.25
Total =		2.00

     So,

Expected number of Heads = 2

So,

Answer is:

2