Question

A coin is tossed six times, then the probability of obtaining heads and tails

alternatively is :

​

Answer 1

The probability of obtaining heads and tails alternatively is 1/32

Given :

A coin is tossed six times

To find :

The probability of obtaining heads and tails alternatively

Solution :

Step 1 of 3 :

Find total number of possible outcomes

A coin is tossed six times

So total number possible outcomes

$\sf = {2}^{6}$

$\sf = 64$

Step 2 of 3 :

Find total number of possible outcomes for the event

Let A be the event that of obtaining heads and tails alternatively

Then possible outcomes for the event A is THTHTH , HTHTHT

So total number of possible outcomes for the event A is 2

Step 3 of 3 :

Find the required probability

Hence the required probability

= P(A)

$\displaystyle \sf{ = \frac{Number \: of \: favourable \: cases \: to \: the \: event \: A }{Total \: number \: of \: possible \: outcomes }}$

$\displaystyle \sf{ = \frac{2}{64} }$

$\displaystyle \sf{ = \frac{1}{32} }$

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