Question

You flip a coin 4 times. Let X be the number of tails that come up. What expression corresponds with the notation PlX<2) = ?What is the probability that there are at most 2 tails?What is the probability that there are at least 2 tails?What is the probability that there is no more than 2 tails?What is the probability that there are fewer than 2 tails?

Answer 1

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:

$P(X<2)=\frac{5}{16}$

The probability that there are atmost 2 tails that means:

$P(X\leq2)=\frac{11}{16}$

The probability that there are atleast 2 tails is given by:

$P(X\ge2)=\frac{11}{16}$

The probability that there is no more than 2 tails is the same as at most 2 tails which is given by:

$P(X\leq2)=\frac{11}{16}$

The probability that there are fewer than 2 tails is the same as less than 2 tails which is given by:

$P(X<2)=\frac{5}{16}$