When tossed, a certain coin has equal probability of landing

Question

When tossed, a certain coin has equal probability of landing on either side. If the coin is tossed 3 times, what is the probability that it will land on the same side each time?

A. 1/8 
B. 1/4 
C. 1/3 
D. 3/8 
E. 1/2

Bunuel · Accepted Answer

Winning scenario is if we'll have either three tails (TTT) or three heads (HHH):

\frac{1}{2}*\frac{1}{2}*\frac{1}{2}+\frac{1}{2}*\frac{1}{2}*\frac{1}{2}=\frac{1}{4} .

Answer: B.

eschn3am · Answer

There are 8 possibilities for outcomes when flipping a fair coin 3 times. 

2*2*2=2^3=8

of these 8 possibilities there are 2 with the coin landing on the same side each time. HHH and TTT.

so the probability is 2/8 or 1/4. 

HHH -- works
HHT
HTH
HTT
THH
THT
TTH
TTT -- works

the standard .5*.5*.5=1/8 but that's just the probability of getting one SPECIFIC side 3 times in a row (ie probability of 3 heads). Since they don't care if it's 3 heads or 3 tails you have to multiply 1/8 by 2 (so now it's the probability of 3 heads OR 3 tails)

Cez005 · Answer

1st throw: Probability of getting either side = 1
2nd throw: Probability of getting the first side = 1/2
3rd throw: Probability of getting the first side = 1/2

(1/2)*(1/2)=1/4

ScottTargetTestPrep · Answer

We need to determine the probability that a coin lands on the same side for all 3 tosses of the coin. This means that the 3-toss outcome will be either H-H-H or T-T-T.

P(T-T-T) = 1/2 x 1/2 x 1/2 = 1/8

P(H-H-H) = 1/2 x 1/2 x 1/2 = 1/8

Thus, the probability that the coin lands on the same side each time is 1/8 + 1/8 = 2/8 = 1/4.

Answer: B

BrentGMATPrepNow · Answer

P(3 matching tosses) = P(ANY result on 1st toss   AND    2nd toss matches 1st toss   AND    3rd toss matches 2nd toss)
= P(ANY result on 1st toss)   x    P(2nd toss matches 1st toss )   x    P(3rd toss matches 2nd toss)
= 1   x    1/2   x    1/2
= 1/4
= B

Cheers,
Brent

AnkurGMAT20 · Answer

@Bunel, GMAT prep question. Please tag it.

Bunuel · Answer

________________________
Done. Thank you!

BrushMyQuant · Answer

We need to find On three consecutive flips of a coin, what is the probability that it will land on the same side each time?

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 B

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 B 
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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When tossed, a certain coin has equal probability of landing

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When tossed, a certain coin has equal probability of landing

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