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Question

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

A
1225
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B
1325
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C
1425
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D
1525
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Solution

The correct option is B 1325
Probability that heads does not occurs two or more times in a row = Probability that head will not appears in any trial or only one head appears or heads will appear in alternative trial.
Therefore,
Case (1): All tail appear
p1=(12)5=125

Case (2): Only one head appear i.e., 4T,1H
p2= 5C4×(12)4×(12)=525

Case (3): heads appear in alternate position (3T, 2H) i.e.,
{__ T __ T __ T __}p3= 4C2×(12)2×(12)3=625
where __ represent places where head can occur.

Case (4): heads appear in alternate position (3H, 2T) i.e., {__ T __ T __}
p4= 3C3×(12)2×(12)3=125

Hence, required probability=1+5+6+125=1325

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