AP EAMCET · Maths · Probability

Tom and Jerry play a game of alternately throwing an unfair coin. First one to get head wins. If Tom starts the game, he has $62.5 %$ chance of winning the game. Suppose this coin is tossed $5$ times, then the probability of getting exactly $3$ heads is

A $\frac{144}{625}$
B $\frac{124}{625}$
C $\frac{121}{625}$
D $\frac{100}{625}$

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Answer & Solution

Correct Answer

(A) $\frac{144}{625}$

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Detailed explanation

Tom and Jerry play a game of alternately throwing an unfair coin. First one to get head wins. The coin is unfair, hence, let, the probability of getting a head when the coin is tossed is x then the probability of getting a tail when the coin is tossed is 1-x. If Tom starts the…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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Tom and Jerry play a game of alternately throwing an unfair coin. First one to get head wins. If Tom starts the game, he has 62.5% chance of winning the game. Suppose this coin is tossed 5 times, then the probability of getting exactly 3 heads is

Step-by-step Solution

Tom and Jerry play a game of alternately throwing an unfair coin. First one to get head wins. If Tom starts the game, he has $62.5 %$ chance of winning the game. Suppose this coin is tossed $5$ times, then the probability of getting exactly $3$ heads is