Multiple choice

Given below are two statements: Statement I: A coin is tossed three times. The probability of getting exactly two heads is 3 8 . Statement II: In tossing of 10 coins, the probability of getting exactly 5 heads is 63 256 . In light of the above statements, choose the correct answer from the options given below.

  1. Both Statement I and Statement II are true.

  2. Both Statement I and Statement II are false.

  3. Statement is true, but Statement II is false.

  4. Statement I is false, but Statement II is true.
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A Correct answer
Explanation

For three tosses, exactly two heads can occur in 3 outcomes out of 8, giving 3/8. For ten tosses, exactly five heads has probability 252/1024 = 63/256, so both statements are true.

AI explanation

Statement I is evaluated using the binomial probability formula for exactly two heads in three tosses, giving 3C2 multiplied by (1/2)^3, which equals 3/8. Statement II is evaluated for exactly five heads in ten tosses, giving 10C5 multiplied by (1/2)^10, which equals 252/1024 or 63/256. Since both calculated probabilities match the given statements, both statements are true.

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