A fair coin is tossed 3 times, what is the probability of at least two consecutive heads

Q: When 3 coins are tossed what is the probability of getting at most 2 heads?

ANS: 7/8. Q. The probability of getting atmost two heads on tossing three coins simultaneously is .

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Sample space for tossing 3coins: HHH,HTH,THH,TTH,HHT,HTT,THT ,TTTTotal number of possible outcomes=8Probability of getting at least two tails is:P(A)=P(gettingtwotails)+P(getting3tails)=38 +18=48=12Therefore, the probability of getting at least 2 tails if you flip a coin 3times is 12.
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When 3 coins are tossed what is the probability of getting at most 2 heads?
When a coin is tossed 3 times what is the probability it will result in 2 heads and 1 tail?
When a coin is thrown 3 times what is the probability that at least one head is obtained 7 8?
When a coin is tossed 3 times what is the probability of getting at least one tail?

Solution

Sample space for tossing 3coins: HHH,HTH,THH,TTH,HHT,HTT,THT ,TTTTotal number of possible outcomes=8Probability of getting at least two tails is:P(A)=P(gettingtwotails)+P(getting3tails)=38 +18=48=12Therefore, the probability of getting at least 2 tails if you flip a coin 3times is 12.

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Matthew D.

asked • 10/07/18

How do I solve this without list out every possibility like HHH, HHT, Etc?

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Paul M. answered • 10/07/18

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You have stated the easiest way, i.e. write down the entire (small) sample space. And the answer is 3/8

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Matthew D.

Thanks!

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Paul M.

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You are welcome.

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10/07/18

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1 Problem
2 Video Solution by OmegaLearn Using Casework
3 Video Solution
4 Solution 1
5 Solution 2
6 See Also

A fair coin is tossed 3 times. What is the probability of at least two consecutive heads?

Video Solution by OmegaLearn Using Casework

https://youtu.be/6xNkyDgIhEE?t=44

~ pi_is_3.14

Video Solution

https://youtu.be/2lynqd2bRZY ~savannahsolver

Solution 1

First, there are

ways to flip the coins, in order.

The ways to get no one head are HHT and THH.

The way to get three consecutive heads is HHH.

Therefore, the probability of flipping at least two consecutive heads is

Solution 2

Let's figure it out using complementary counting.

First, there are

ways to flip the coins, in order. Secondly, what we don't want are the ways without getting two consecutive heads: TTT, HTH, and THT. Then we can find out the probability of these three ways of flipping is

,and

, respectively. So the rest is exactly the probability of flipping at least two consecutive heads:

. It is the answer

. ----LarryFlora

2013 AMC 8 (Problems • Answer Key • Resources)
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When 3 coins are tossed what is the probability of getting at most 2 heads?

ANS: 7/8. Q. The probability of getting 'atmost two heads' on tossing three coins simultaneously is .

When a coin is tossed 3 times what is the probability it will result in 2 heads and 1 tail?

The Probability of getting two heads and one tails in the toss of three coins simultaneously is 3/8 or 0.375.

When a coin is thrown 3 times what is the probability that at least one head is obtained 7 8?

We have to find the probability of getting at least one head. We observe that there is only one scenario in throwing all coins where there are no heads. The chances for one given coin to be heads is 1/2. Therefore, the probability of getting at least one head is 7/8.