On three consecutive flips of a coin, what is the probabilit

Question

On three consecutive flips of a coin, what is the probability that all three produce the same result?

(A) 1/16
(B) 1/8
(C) 1/4
(D) 3/8
(E) 1/2

I came up with (1/2)*(1/2)*(1/2) =1/8

However, the explanation states that the answer is 1/4.

On the Total GMAT book, I had the following question: If a fair coin is flipped three times, what is the probability that it will be heads all three times?

There the answer given is 1/8, which is what I came up with.

Am I missing something? I do not see any distinction between these two questions.

Bunuel · Accepted Answer

TTT case --> P = (1/2)^3 = 1/8.
HHH case --> P = (1/2)^3 = 1/8.

P(TTT or HHH) = 1/8 + 1/8 = 1/4.

Answer: C.

BrentGMATPrepNow · Answer

APPROACH #1   
P(3 identical flips) = P(1st flip is ANY side   AND   2nd flip matches 1st flip   AND   3rd flip matches 1st flip)
= P(1st flip is ANY side)   x   P(2nd flip matches 1st flip)   x   P(3rd flip matches 1st flip)
= 1   x   1/2   x   1/2
= 1/4
Answer: C

APPROACH #2   
P(3 identical flips) = P(3 heads in a row    OR    3 tails in a row) 
= P(3 heads in a row)    +    P(3 tails in a row) 
= P(1st flip is heads   AND   2nd flip is heads   AND   3rd flip is heads)    +    P(1st flip is tails   AND   2nd flip is tails   AND   3rd flip is tails) 
=   x   P(2nd flip is heads)   x   P(3rd flip is heads)]    +      x   P(2nd flip is tails)   x   P(3rd flip is tails)]
=   x   1/2   x   1/2]    +      x   1/2   x   1/2]
1/8    +    1/8
= 1/4
Answer: C

fatimaba · Answer

Why isn't "B" the answer?

blueseas · Answer

probability for head =  1/2 
similarly probability for tails =  1/2

case 1: all 3 times = head
in that case 
probability  = 1/2*1/2*1/2 = 1/8

case 2 : all tails then again probability will be  1/8

so total probability will be  1/8+1/8 = 1/4

hope it helps

MartyTargetTestPrep · Answer

If they had to all three be heads, then the calculation would be 1/2 * 1/2 * 1/2 = 1/8

In addition to getting the chosen outcome if we get three heads, we know that also we have success if the the three are all tails. So right there you know that the probability is greater than the 1/8 for three heads.

How much greater?

Well we have success if they are all heads. The probability of that is 1/8.

We also have success if they are all tails. The probability of that is also 1/8.

So we add the two together for the total probability of success, which is 1/8 + 1/8 = 1/4, choose  C .

dabaobao · Answer

TL;DR

HHH or TTT
Possible Cases: 2
Total Cases: 2^3 = 8
P = 2/8 = 1/4

or P = 1 * 1/2 * 1/2 = 1/4
ANSWER: C

Veritas Prep Official Solution

The trap answer here is 1/8 – you might look at this as a 1/2 probability on the first flip, then a 1/2 on the second, and a 1/2 on the third for a 1/8 probability, but remember – in this case the result of the first flip doesn’t have to be one or the other. Your job is just to match whatever the first result was on the next two. If the first was heads, then you need heads next (a 1/2 chance) and heads again (a 1/2 chance). And if it were tails, then you need tails (1/2) then tails (1/2). But because “any match will do” and you don’t care that it’s a specific match – the question doesn’t specify all heads or all tails, just “all of one of them” – your probability doubles because you’re not concerned about the result of the first event, you’re only concerned about matching whatever that result was.

General Tips  
Credit: Veritas Prep

So for probability questions that ask about pairs or matches, remember:

1) Check whether you need a *specific* pair/match or not.

2) If you don’t need a specific pair, but “any pair will do,” then the probability of the first result is 100% – something will happen.

3) If you need to guess, keep in mind that if it’s an unspecified pair/match, it’s almost certain that one of the trap answers will be a smaller number than the correct answer (in the above case, 1/8 is a trap and 1/4 is correct), so you can confidently rule out the smallest number and use number properties to try to eliminate another 1-2 answers.

Basshead · Answer

Probability of getting heads or tails on the first coin: 1

Probability of getting a matching result on the second coin: 1/2

Probability of getting a matching result on the third coin: 1/2

1 * 1/2 * 1/2 = 1/4

BrushMyQuant · Answer

We need to find On three consecutive flips of a coin, what is the probability that all three produce the same result?

Coin is tossed 3 times => Total number of cases =  2^3  = 8

Lets solve the problem using two methods

Method 1:

Out of the 8 cases there are only two cases in which all the outcomes are same. HHH and TTT.

=>  Probability that all three produce the same result  =  \frac{2}{8}  =  \frac{1}{4}

So,  Answer will be C

Method 2:

Let's find out the number of cases. 
In the first toss we can get anything out of head or tail in 2 ways
In second toss we need to get the same value (head or tail) as we got in the first toss => 1 way
In third toss we need to get the same value (head or tail) as we got in the second toss => 1 way

=> Total number of ways = 2*1*1 = 2 ways

=>  Probability that all three produce the same result  =  \frac{2}{8}  =  \frac{1}{4}

So,  Answer will be C 
Hope it helps!

Watch the following video to learn How to Solve Probability with Coin Toss Problems

https://www.youtube.com/watch?v=LRURv38kZw8

bumpbot · Answer

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On three consecutive flips of a coin, what is the probabilit

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On three consecutive flips of a coin, what is the probabilit

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