Complete the following probability distribution table and then calculate the stated probabilities. HINT [See Quick Example 5.]
Outcome | a | b | c | d | e |
---|---|---|---|---|---|
Probability | 0.1 | 0.01 | 0.4 | 0.09 |
(a) P({a, c, e})
P({a, c, e}) =
(b) P(E ∪ F),
where E = {a, c, e} and F = {b, c, e}
P(E ∪ F) =
(c) P(E'), where
E is as in part (b)
P(E') =
(d) P(E ∩ F ),
where E and F are as in part (b)
P(E ∩ F) =
a) The sum of all the probabilities would be 1. Hence,
0.1 + 0.01 + 0.4 + 0.09 + P(e) = 1
0.6 + P(e) = 1
P(e) = 0.4
Hence,
P({a, c, e}) = 0.1 + 0.4 + 0.4 = 0.9
b) P(E U F) = P(a, b, c , e) = 1 - P(d) = 1 - 0.09 = 0.91
c) P(E') = 1 - P(E) = 1 - 0.9 = 0.1
d) P(E F) = P(c, e) = 0.4 + 0.4 = 0.8
Complete the following probability distribution table and then calculate the stated probabilities. HINT [See Quick Example...
Complete the following probability distribution table and then calculate the stated probabilities. HINT [See Quick Example 5.] Outcome a b c d e Probability 0.1 0.09 0.5 0.01 _____ (a) P({a, c, e}) P({a, c, e}) = (b) P(E ∪ F), where E = {a, c, e} and F = {b, c, e} P(E ∪ F) = (c) P(E'), where E is as in part (b) P(E') = (d) P(E ∩ F ), where E and F are as in...
Complete the following probability distribution table and then calculate the stated probabilities. HINT [See Quick Example 5.] Outcome a b c d e Probability 0.1 0.05 0.4 0.05 (a) P({a, c, e}) P({a, c, e}) = (b) P(E ∪ F), where E = {a, c, e} and F = {b, c, e} P(E ∪ F) = (c) P(E'), where E is as in part (b) P(E') = (d) P(E ∩ F ), where E and F are as in part (b) P(E ∩ F)...
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