Multiple choice

Two dice are tossed $6$ times, then the probability that $7$ will show an exactly four of tosses is

  1. $\dfrac {225}{18442}$
  2. $\dfrac {116}{20003}$
  3. $\dfrac {125}{15552}$

  4. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Probability of getting a 7 with two dice is 6/36 = 1/6. Probability of not getting a 7 is 5/6. Using binomial distribution for 4 successes in 6 trials: 6C4 * (1/6)^4 * (5/6)^2 = 15 * (1/1296) * (25/36) = 375 / 46656 = 125 / 15552.

AI explanation

Using the binomial distribution formula, the probability is given by nCr multiplied by p to the power of r multiplied by q to the power of n minus r. The probability p of rolling a 7 is 6/36, or 1/6, and q is 5/6. For 4 successes in 6 trials, the calculation is 6C4 multiplied by (1/6)^4 multiplied by (5/6)^2, which simplifies to 15 multiplied by 1/1296 multiplied by 25/36, giving 125/15552.

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