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Question

A fair coin is tossed  a fixed number of times.  If the probability of getting 7 heads is equal to that getting 9 heads, then the probability of getting 3 heads is
  1. 35212
  2. 35214
  3. 7212
  4. 7214


Solution

The correct option is A 35212
Probability of r successes in n trials is equal to nCrprqnr, where p is the probability of success in one trial and q is the probability of failure in one trial. 
Let the coin be tossed n times. Here p and q are both 1/2 
P(getting 7 heads)=nC7(12)n andP(getting 9 heads)=nC9(12)nGiven, P(7 heads)=P(9 heads) nC7=nC9n=16P(3 heads)=16C3(12)16=35212.

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