(i) Using Bernoulli’s Trial P(Success=x) \(=n_{C_x}.p^x.q^{(n-x)}\)
x = 0, 1, 2, ………n and q = (1 - p), n = 7
The favourable outcomes,
(1,6), (6,1), (2,5), (5,2), (3,4), (4,3)
The probability of success \(=p=\frac{6}{36}=\frac{1}{6}\)
q = \(\frac{5}{6}\)
probability of no success \(=7_{C_0}.(\frac{1}{6})^0(\frac{5}{6})^7\)
\(\Rightarrow\)\((\frac{5}{6})^7\)
(ii) Using Bernoulli’s Trial P(Success=x) \(=n_{C_x}.p^x.q^{(n-x)}\)
x = 0, 1, 2, ………n and q = (1 - p), n = 7
the favourable outcomes,
(1,6), (6,1), (2,5), (5,2), (3,4), (4,3)
The probability of success \(=p=\frac{6}{36}=\frac{1}{6}\)
q = \(\frac{5}{6}\)
probability of exactly 6 successes \(=7_{C_6}.(\frac{1}{6})^6(\frac{5}{6})^1\)
\(\Rightarrow\) \(35.(\frac{1}{6})^7\)
(iii) Using Bernoulli’s Trial P(Success=x) \(=n_{C_x}.p^x.q^{(n-x)}\)
x = 0, 1, 2, ………n and q = (1 - p), n = 7
the favourable outcomes,
(1,6), (6,1), (2,5), (5,2), (3,4), (4,3)
The probability of success \(=p=\frac{6}{36}=\frac{1}{6}\)
q = \(\frac{5}{6}\)
probability of at least 6 successes =
(iv) Using Bernoulli’s Trial P(Success=x) \(=n_{C_x}.p^x.q^{(n-x)}\)
x = 0, 1, 2, ………n and q = (1 - p), n = 7
the favourable outcomes,
(1,6), (6,1), (2,5), (5,2), (3,4), (4,3)
The probability of success \(=p=\frac{6}{36}=\frac{1}{6}\)
q = \(\frac{5}{6}\)
probability of at least 6 successes =
