SOLUTION: What is the probability of NOT tossing 3 heads with 3 fair coins?

Question 313330: What is the probability of NOT tossing 3 heads with 3 fair coins?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
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.

RELATED QUESTIONS
10 fair coins are tossed,then what is the probability of 3 heads obtained at most? (answered by Fombitz)

In toasting three fair coins at once. what is the probability of getting 1. at most two... (answered by Fombitz)

Four fair coins are flipped. What is the probability of getting three or more... (answered by richard1234)

Daniel tosses four fair coins. What is the probability that all four coins will land... (answered by derangoj)

If a fair coin is tossed 3 times, what is the probability of getting at least 2 heads (at (answered by stanbon)

Twelve fair coins are tossed all at once. What is the probability that exactly 5 of... (answered by stanbon)

Five identical and unbiased coins are shaken. What is the probability of obtaining 3... (answered by sudhanshu_kmr,stanbon)

A fair coin is tossed 5 times. What is the probability of obtaining exactly 3 heads. Pick (answered by Fombitz)

A fair coin is tossed 3 times. What is the probability of at least two consecutive... (answered by Boreal)

What is the probability of getting between 3 and 6 heads in 10 tosses of a fair... (answered by stanbon,solver91311)