Multiple choice

A pair of dice is thrown $7$ times. If getting at total of $7$ is considered a success, what is the probability of getting at most $6$ successes?

  1. ${ \left( \cfrac { 5 }{ 6 } \right) }^{ 7 }$
  2. ${ \left( \cfrac { 1 }{ 6 } \right) }^{ 7 }$
  3. $1-{ \left( \cfrac { 1 }{ 6 } \right) }^{ 7 }$

  4. none of these
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C Correct answer
Explanation

The probability of getting a sum of 7 with two dice is 6/36 = 1/6. This is a binomial distribution problem with n=7, p=1/6, q=5/6. The probability of at most 6 successes is 1 minus the probability of 7 successes, which is 1 - (1/6)^7.

AI explanation

Using the binomial distribution, the probability of rolling a sum of 7 on two dice is 6 divided by 36, which equals 1 over 6, making the probability of failure 5 over 6. The probability of getting at most 6 successes in 7 throws is equivalent to 1 minus the probability of getting exactly 7 successes. This gives 1 minus the quantity of 1 over 6 raised to the power of 7, resulting in 1 minus the fraction 1 over 6 raised to the power of 7.

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