Question 313330
It would be 1 minus the probability of tossing 3 heads with 3 fair coins.


The probability of getting a head on one toss is equal to 1/2.


The probability of getting a tail on one toss is equal to 1/2.


The probability of tossing 3 heads with 3 fair coins is:


1/2 * 1/2 * 1/2


That probability becomes 1/8


the probability of NOT tossing 3 heads would then be 1 - 1/8 = 7/8


That probability can also be determined the hard way as follows:


If you don't toss 3 heads in a row, then you can toss:


0 heads out of 3 tosses, or 1 head out of 3 tosses, or 2 heads out of 3 tosses.


The probability of tossing 0 heads out of 3 tosses is the same as the probability of tossing 3 heads out of 3 tosses.   That equals 1/8.


the probability of tossing 1 head out of 3 tosses is:


1/2 * 1/2 * 1/2 * 3 = 1/8 * 3 = 3/8


This itself is the probability of tossing:


htt or tht or tth


Since tossing 1 head out of 3 tosses can happen in 3 ways, and the probability for each of those ways is the same, you need to multiply the probability by 3.


The probability of htt is 1/2 * 1/2 * 1/2 = 1/8
The probability of tht is 1/2 * 1/2 * 1/2 = 1/8
the probability of tth is 1/2 * 1/2 * 1/2 = 1/8


The probability of tossing 2 heads out of 3 tosses becomes 3/8 as well.


You get:


hht = 1/2 * 1/2 * 1/2 = 1/8
hth = 1/2 * 1/2 * 1/2 = 1/8
thh = 1/2 * 1/2 * 1/2 = 1/8

Total is 3/8.


The probability of not getting 3 heads in 3 tosses is therefore.


p(0 heads) = 1/8
p(1 head) = 3/8
p(2 heads) = 3/8


Total probability of p(0 or 1 or 2) = p(0) + p(1) + p(2) = 1/8 + 2/8 + 3/8 = 7/8


The easy way was to take 1 minus the probability of 3 heads which we did up top.


You get the same answer.