Multiple choice

A symmetrical die is rolled $6$ times. If getting an odd number is a success, the probability of atmost $5$ successes is

  1. $\dfrac{60}{64}$
  2. $\dfrac{63}{64}$
  3. $\dfrac{120}{164}$
  4. $\dfrac{10}{14}$
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B Correct answer
Explanation

Probability of success (odd number) p = 1/2. n = 6. P(at most 5) = 1 - P(6 successes) = 1 - (1/2)^6 = 1 - 1/64 = 63/64.

AI explanation

The probability of an odd number on a die is 3/6, which is 1/2. Using the binomial distribution, the probability of at most 5 successes is 1 minus the probability of 6 successes. Therefore, the required probability is 1 - (1/2)^6, which is 1 - 1/64, or 63/64.

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