GATE Mechanical Engineering (ME) 2018 Shift 2 Solved Paper

Question : 8 of 65

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An unbiased coin is tossed six times in a row and four different such trials are conducted. One trial implies six tosses of the coin. If

{H}

stands for head and

{T}

stands for tail, the following are the observations from the four trials:
(1) HTHTHT
(2) TTHHHT
(3) HTTHHT
(4) HHHT
Which statement describing the last two coin tosses of the fourth trial has the highest probability of being correct?

Two T will occur.
One H and one T will occur.
Two H will occur.
One H will be followed by one T .

Validate

Solution:

Since the coin is unbiased, the probability of getting heads is equal of tail.
In unbiased coin previous trials does not matter
Probability of getting both heads

=\;{1}/{2} × \;{1}/{2}=1 / 4

Probability of getting a head and a tail(

{HT}+ {TH})=2 × \;{1}/{2} × \;{1}/{2}=1 / 2

Probability of getting both tails

=\;{1}/{2} × \;{1}/{2}=1 / 4

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