Answer:
(i) The probability of at least 2 successes is 0.2093.
(ii) The probability of at least one but no more than 3 successes is 0.9548.
Step-by-step explanation:
Now the total number of cases = {1, 2, 3, 4, 5, 6} = 6.
Favourable cases = {1, 6} = 2.
[tex]p = \frac{2} {3} = \frac{1} {3} \\\\q = 1- p\\\\q = \frac{2}{3} \\\\n=5[/tex]
i) at least 2 successes,
[tex]P(X\geq 2) = (^{n}C_{x} )\times p^{x} \times (1-p)^{n-x}\\\\P(X\geq 2) = 0.2093[/tex]
ii) at least one but no more than 3 successes,
[tex]P(X\leq 3) = (^{n}C_{x} )\times p^{x} \times (1-p)^{n-x}\\\\P(X\leq 3)= 0.9548[/tex]
