Question

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

A. \(\big(\frac{5}{7}\big)^7\)

B. \(\big(\frac{1}{6}\big)^7\)

C. \(\big(1-\frac{1}{6^7}\big)\)

D. None of these

Answer 1

Using Bernoulli’s Trial P(Success=x) \(=n_{C_x}.p^x.q^{(n-x)}\)

x = 0, 1, 2, ………n and q = (1 - p), here n = 7

As we know that the favourable outcomes of getting at most 6 success are, successes will be, getting a total of 7 is success, i.e.,

We can get 7 by, (1,6), (2,5), (3,4), (4,3), (5,2), (6,1)

p = \(\frac{6}{36},\) q = \(\frac{30}{36}\)

The probability of success is \(\frac{1}{6}\) and of failure is also \(\frac{5}{6}\)

\(=\frac{The\,favourable\,outcomes}{The\,total\,number\,of\,outcomes}\)

The probability of getting at most 6 successes =