KVPY SX SB Exam 05-Nov-2017 Question Paper

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Question : 16 of 120

Marks: +1, -0

If a fair coin is tossed 5 times, the probability that heads does not occur two or more times in a row is

$12/2^5$
$13/2^5$
$14/2^5$
$15/2^5$

Solution:

Case (1) : All tail

(1/2)^5

Case (2) : 4T, 1H

^5C_4(1/2)^4..(1/2)^5=5/2^5

Case (3) :

\times T \times T \times T \times

(1/2)^3×^4C_2×(1/2)^2=1/2^5×6=6/2^5

Case (4) :

\times T \times T \times

(1/2)^2×(1/2)^3=1/2^5

overall

13/2^5

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