If you flip a fair coin 4 times, what is the probability that you will get exactly 2 tails?

Question

57705 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-03-30T01:21:36

$P("Exactly 2H") = 0.375$

Method 1 - Tree Diagram

enter image source here

$P("Exactly 2H") = P("HHTT") + P("HTHT") +$
$" " P("HTTH") + P("TTHH") +$
$" " P("THHT") + P("THTH")$
$" " = 0.0625 * 6$
$" " = 0.375$

Method 1 - Combinations

Using the combination formula:

$""_nC^r = ( (n), (r) ) = (n!)/(r!(n-r)!)$

We seek any combination of 2 heads from 4 coins:

$n("possible combinations") = ""_2C^4 = ( (4), (2) )$
$" " = (4!)/(2!(4-2)!)$
$" " = (4!)/(2!2!)$
$" " = (24)/(2*2)$
$" " = 6$

And the total number of all combinations of 4 flips

$n("total combinations") = 2^4$
$" " = 16$

$P("Exactly 2H") = 6/16$
$" " = 0.375$