# Question 397e3

Feb 25, 2017

The question does not specify whether it is EXACTLY 2 tails, or if more than 2 tails can be included as well (at least 2 tails).

There are only $8$ possible combinations of heads and tails:
(Considering different orders)

$3 \text{ heads "color(white)(.................................)"HHH}$
$2 \text{ heads "and 1 " tail "color(white)(...........) "HHT,HTH,THH}$
1 " tail " and 2 " heads"color(white)(.............)color(blue)("TTH, THT, HTT")
$3 \text{ tails "color(white)(..................................)"TTT}$

The probability has to be given as a fraction out of $8$

There are $3$ ways out of the $8$ of getting exactly 2 tails

$P \left(2 \text{ tails}\right) = \frac{\textcolor{b l u e}{3}}{8}$

If there can be 2 or more tails:

$3 \text{ heads "color(white)(.................................)"HHH}$
$2 \text{ heads "and 1 " tail "color(white)(...........) "HHT,HTH,THH}$
1 " tail " and 2 " heads"color(white)(.............)color(blue)("TTH, THT, HTT")
3 " tails "color(white)(..................................)color(blue)("TTT")

P( "at least 2 tails") = color(blue)(4)/8 = 1/2" "# in the simplest form.

The un-simplified denominator cannot be anything else but 8, because that is the total number of possibilities.