When three coins are tossed together the probability that all coins have the same face up is

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Submitted by examrobotsa on

Q: 137 (IAS/1997)
When three coins are tossed together the probability that all coins have the same face up is

question_subject: 

Maths

question_exam: 

IAS

stats: 

0,5,8,3,3,5,2

keywords: 

{'probability': [0, 3, 3, 0], 'coins': [2, 0, 1, 1], 'same face': [1, 1, 1, 0]}

When three coins are tossed together, there are eight possible outcomes: {HHH, HHT, HTH, THH, TTH, THT, HTT, TTT}. In these outcomes, only two cases satisfy the condition that all coins have the same face up: {HHH, TTT}. Thus, the probability that all coins have the same face up is 2/8 = 1/4.

Option-1 indicates the probability of 1/3, which is not possible because it would require eight to be divisible by three, which it is not. Option-2 gives the probability as 1/6 which is also incorrect since we have eight outcomes not six. Option-4 implies there are 12 outcomes which is wrong. The correct answer is option-3 which correctly states the probability is 1/8.