If a coin is tossed 4 times and X is the number of tails that come up then the sample space for the problem has 16 points given as:
S={HHHH,HHHT,HHTH,HTHH,THHH,TTHH,THTH,HTHT,HHTT,THHT,HTTH,TTTH
TTHT,THTT,HTTT,TTTT,
There are 16 sample points.
The probability that X<2 is given by:
The probability that there are atmost 2 tails that means:
The probability that there are atleast 2 tails is given by:
The probability that there is no more than 2 tails is the same as at most 2 tails which is given by:
The probability that there are fewer than 2 tails is the same as less than 2 tails which is given by: