If four coins are tossed, what is the probability that the result will be two heads and two tails?
2007-07-10 10:29:26 · 4 answers · asked by nick1995 1 in Science & Mathematics ➔ Mathematics
This is the third term of the binomial expansion of
(p+q)^4 where p and q are 0.5, which is
6 * 0.0625 = 0.375
2007-07-10 10:41:24 · answer #1 · answered by cattbarf 7 · 1⤊ 0⤋
When four fair coins are flipped, there are 2^4 = 16 outcomes (if the order matters). Each outcome has a 1/16 probability. So, we simply count the number of outcomes that end with 2 heads and 2 tails, then divide by 16:
HHTT
TTHH
HTHT
THTH
HTTH
THHT
There are
4! / (2! * 2!)
= 24 / (2 * 2)
= 24 / 4
= 6
ways to flip 2 heads and 2 tails, out of 16 total. So the probability is 6/16, or 3/8.
2007-07-10 17:39:06 · answer #2 · answered by lithiumdeuteride 7 · 0⤊ 0⤋
By exhaustion, all possibilities are:
HHHH
HHHT
HHTH
HHTT
HTHH
HTHT
HTTH
HTTT
THHH
THHT
THTH
THTT
TTHH
TTHT
TTTH
TTTT
Out of these 16 possibilities, 6 are 2 each heads n' tails.
6/16 = 0.375
2007-07-10 17:38:17 · answer #3 · answered by Gary H 6 · 1⤊ 1⤋
(0.5^4)(4!)/(2!2!)
2007-07-10 17:38:48 · answer #4 · answered by swd 6 · 1⤊ 0⤋