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Question

A fair coin is tossed a fixed number of items. If the probability of getting7 heads is equal to that of getting 9 heads, then the probability of getting 3 heads is


A

35212

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B

35214

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C

7212

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D

None of these

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Solution

The correct option is A

35212


Explanation for correct option:

Step-1: Define events:

Number of times coin tossed =n

Probability of getting heads 'p'=12

Probability of getting tails 'q'=12[p+q=1]

Step-2 : Calculate the value of 'n'

As per the condition given

Probability of getting seven heads =Probability of getting nine heads

Crn12712n-7=C9n12912n-9[Crnprqn-r]

C7n12n=C9n12nC7n=C9nn=7+9[Crn=Cr+1nn=r+r+1]n=16

Step3. Probability of getting three heads:

Substitute the value of n=16,r=3 in Crnprqn-r

C3161231216-3

=C3161216=16!16-3!3!1216Crn=n!(n-r)!r!=35212

Hence, option(A) is the correct answer.


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