SOLUTION: A fair coin is tossed four times. What is the probability of obtaining a.exactly one head b.Tails on each of the first 3 tosses c.Four heads

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Question 866989: A fair coin is tossed four times. What is the probability of obtaining
a.exactly one head
b.Tails on each of the first 3 tosses
c.Four heads
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
H = heads
T = tails


Here are all of the ways to toss a coin 4 times


No Tails (count = 1)
HHHH

1 Tail (count = 4)
HHHT
HHTH
HTHH
THHH

2 Tails (count = 6)
HHTT
HTHT
THHT
THTH
TTHH
HTTH

3 Tails (count = 4)
TTTH
TTHT
THTT
HTTT

4 Tails (count = 1)
TTTT


Alternatively, you can use a tree diagram to get that list above


(Image Source: http://www.learner.org/courses/learningmath/data/session8/part_c/probability.html)


Add up the counts to get 1+4+6+4+1 = 16. Notice this sequence of numbers is found in pascals triangle (look in the row: 1, 4, 6, 4, 1)


Let's use this info to answer the 3 part question

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a) What is the probability of obtaining exactly one head?


Look under the section "3 tails" and you'll see that there are 4 instances where this happens: TTTH, TTHT, THTT, HTTT


Getting 3 tails is the same as getting 1 head. This is out of 16 total ways to flip a coin 4 times. So the probability is 4%2F16+=+1%2F4


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b) What is the probability of obtaining tails on each of the first 3 tosses


That only happens 2 times. Once in the "3 tails" section which is TTTH and once in the "4 tails" section, which is TTTT. So the probability is 2%2F16+=+1%2F8


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c) What is the probability of obtaining four heads


This only happens once in the "no tails" section (ie the "four heads" section). So the probability is 1%2F16