If a coin has an equal probability of landing heads up or tails up eac

Question

If a coin has an equal probability of landing heads up or tails up each time it is flipped, what is the probability that the coin will land heads up exactly twice in 3 consecutive flips?

(A) 0.125
(B) 0.25
(C) 0.375
(D) 0.50
(E) 0.666

Archit3110 · Answer

total fair chances ; 1/2*1/2*1/2 = 1/8 ; .125
and getting heads twice in 3 flips we have 
HHT; HTH; THH ; 3 ways so .125*3 ; .375
IMO C

SiffyB · Answer

P(getting heads) = P(getting tails) = 0.5 (50%)

We have to determine the probability of getting exactly 2 Heads in three consecutive flips. Therefore, we have H, H and T. We have to see the possible cases.
1) HTH
2) HHT
3) THH

Thus, total test cases with exactly 2 H are: 3

Also, the total cases will be 8.
P(H=O) + P(H=1) + P(H=2) + P(H=3)
= 1 + 3 + 3 + 1
= 8

Thus, the required probability = 3/8= 0.375

(C)

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Mohammadmo · Answer

3C2×(1/2)²×1/2=3/8=0.375
Option C

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SvelteNigerian · Answer

Hello, thanks for the solution.

Kindly explain why we have to consider 3 different scenarios for the flips.

I assumed that one flip is when we get either a head or a tail and that we have adequately covered the 3 consecutive flips by 1/2*1/2*1/2 = 1/8

Why then are we considering 3 different flips when the question hasn't explicitly told us that 3 different events took place?

Thanks

Kritisood · Answer

Hi

first, we calculate the probability of getting 3 heads = (1/2)^2 = 1/8 then we account for the  order  of heads in each toss HHT = 3!/2! = 3 therefore 1/8*3=3/8=0.375

CEdward · Answer

If a coin has an equal probability of landing heads up or tails up each time it is flipped, what is the probability that the coin will land heads up exactly twice in 3 consecutive flips?

(A) 0.125
(B) 0.25
(C) 0.375
(D) 0.50
(E) 0.666

Possibilities:

HHT
THH
HTH

Each possibility has a 1/2 x 1/2 x 1/2 = 1/8 chance of happening

1/8 + 1/8 + 1/8 = 3/8 = 0.375

C

BrushMyQuant · Answer

Given that A fair coin is tossed three times, and we need to find what is the probability that the coin will land heads up exactly twice

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

Out of these 8 cases following are the cases in we will get exactly two heads
THH, HTH, HHT
=> 3 cases

=> Probability that the coin will land heads up exactly twice =  \frac{3}{8}  = 0.375

So,  Answer will be C 
Hope it helps!

Playlist on Solved Problems on Probability  here

Watch the following video to MASTER Probability with Coin Toss Problems

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

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If a coin has an equal probability of landing heads up or tails up eac

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