Question

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

Answer 1

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

Explanation:

Method 1 - Tree Diagram

`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`