3-a coin is tossed three times, what is the probability of tossing exactly two heads?

1 Answer
Mar 3, 2016

#3/8#

Explanation:

Since 3 is a small number, let's list out all possible combinations.

#color(green){H}# represents a head while #color(red){T}# represents a tail.

#color(blue){3" Heads"}#

#color(green){HHH}#

#color(blue){2" Heads"}#

#color(green){HH}color(red){T}#
#color(green){H}color(red){T}color(green){H}#
#color(red){T}color(green){HH}#

#color(blue){1" Head"}#

#color(green){H}color(red){T T}#
#color(red){T}color(green){H}color(red){T}#
#color(red){T T}color(green){H}#

#color(blue){0" Head"}#

#color(red){T T T}#

The answer is #frac{3}{1+3+3+1} = 3/8#.

In general, you will find that the list resembles a particular row of the pascal's triangle.

www.cut-the-knot.org

If you want to know what is the probability of getting #r# heads (or tails) out of #n# flips, it is the #r^{"th"}# element in the #n+1# row, divided by the sum of all the elements in the #n+1# row. Mathematically, the expression is

#frac{((n),(r))}{2^n} = frac{n!}{r! xx (n-r)! xx 2^n}#

In this case, #n = 3# and #r = 2#.

So

#frac{3!}{2! xx 1! xx 2^3} = frac{6}{2 xx 1 xx 8}#

#= 3/8#