Coin tossing probability statements

CMAT 2021 · Quantitative Techniques & Data Interpretation · Easy · Probability

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 the light of the above statements, choose the correct answer from the options given below.

  1. A.

    Both Statement I and Statement II are true

  2. B.

    Both Statement I and Statement II are false

  3. C.

    Statement is true but Statement II is false

  4. D.

    Statement I is false but Statement II is true

Answer

A

Explanation

Statement I: P(X=2)=(32)(12)3=3×18=38P(X=2) = \binom{3}{2}\left(\frac{1}{2}\right)^3 = 3 \times \frac{1}{8} = \frac{3}{8}. True.

Statement II: P(X=5)=(105)(12)10=2521024=63256P(X=5) = \binom{10}{5}\left(\frac{1}{2}\right)^{10} = \frac{252}{1024} = \frac{63}{256}. True.

Both statements are true.

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