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
The correct option is A35212 Probability of r successes in n trials is equal to nCrprqn−r, 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(getting7heads)=nC7(12)nandP(getting9heads)=nC9(12)nGiven,P(7heads)=P(9heads)⇒nC7=nC9⇒n=16∴P(3heads)=16C3(12)16=35212.