Multiple choice

A die is thrown $7$ times. The chance that an odd number turns up exactly 4 times, is given by

  1. $\dfrac{1}{{128}}$
  2. $\dfrac{{35}}{{128}}$
  3. $\dfrac{1}{2}$
  4. $\dfrac{{31}}{{128}}$
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B Correct answer
Explanation

This is a binomial probability problem with n=7, k=4, and p=0.5. The probability is calculated as C(7, 4) * (0.5)^4 * (0.5)^3, which equals 35 * (0.5)^7 = 35/128.

AI explanation

The probability of getting an odd number on a single die throw is 3/6, which simplifies to 1/2. Applying the binomial distribution formula, the probability of getting exactly 4 odd numbers in 7 throws is 7C4 multiplied by (1/2) to the power of 4 multiplied by (1/2) to the power of 3. This evaluates to 35 multiplied by (1/16) multiplied by (1/8), giving a final result of 35/128.

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