Answer: (i) 15% (ii) 0.6%
<u>Step-by-step explanation:</u>
Given: P(A) = 0.3 ⇒ ~P(A) = 0.7
P(B) = 0.3 ⇒ ~P(B) = 0.7
P(A ∪ B) = 0.6 ⇒ ~P(A ∪ B) = 0.4
If you don't have a calculator function for the Binomial Formula, the equation is: where
- n is the number of trials
- p is the probability of success
- X is the number of successes
(i) Probability of at least 5 --> P(X ≥ 5) means P(5) + P(6) + P(7) + P(8) + P(9) + P(10)
P(5): n = 10, p = 0.3, X = 5 → P(5) = 0.1029
P(6): n = 10, p = 0.3, X = 6 → P(6) = 0.0368
P(7): n = 10, p = 0.3, X = 7 → P(7) = 0.0090
P(8): n = 10, p = 0.3, X = 8 → P(8) = 0.0014
P(9): n = 10, p = 0.3, X = 9 → P(9) = 0.0001
P(10): n = 10, p = 0.3, X = 10 → P(10) =<u> 0.0000 </u>
TOTAL = 0.1502 → 15.02%
(ii) Probability of A or B = 10 --> P(X = 10)
P(10): n = 10, p = 0.6, X = 10 → P(10) = 0.0060 → 0.6%
