Math Ex. (Probability)

小芝芝

2013-02-16 10:31 pm

Can you help me to slove the following questions

1. A letter is selected from the word 'EXAMINATION' . Find the probabilities
that the letter selected is
a) a consonant or 'A'
b) a vowel or 'N'

2. Find A∩B and A∪B for each of the following sets A and B.
a) A={6, 12, 18, 24, 30, 36, 42, 48},
B={8, 16, 24, 32, 40, 48}

b) A={a, e, i, o, u},
B={s, i, n, g, u, l, a, r}

3. From the past experience, the probability of failing of each engine of a
two-engine airplane during a flight is 0.02. Suppose the failure of an engine is
independent of the other. During a flight, find the probabilities that
a) no engines will fail
b) exactly one of the engines will fail
c) at least one of the engines will fail

4. for two events A and B, if P(A)=1/3, P(B)=1/4 and P(A∩B)=1/6, find
a) P(A/B)
b) P(B/A)

回答 (1)

賣女孩的火柴

2013-02-17 3:09 am

✔ 最佳答案

1.
a)
6 vowels : E, 2A, 2I, O
5 consonants : X, M, 2N, T
Total : 11 letters

P(consonant or 'A')
= P(consonant) + P('A')
= (5/11) + (2/11)
= 7/11

b)
P(vowel or 'N')
= P(vowel) + P('N')
= (6/11) + (2/11)
= 8/11

2.
a)
A∩B = {24, 48}
AUB= {6, 8, 12, 16, 18,24, 30, 32, 36, 40, 42, 48}

b)
A∩B = {a, i, u}
AUB= {a, e, I, o, u, s, n,g, l, r}

3.
(a)
F : an engine fails
N : an engine does not fail

P(no engines fail)
= P(N and N)
= (1 - 0.02)²
= 0.9604

(b)
P(exactly one engine fails)
= P(F and N) + P(N and F)
= 0.02 x (1 - 0.02) + (1 - 0.02) x 0.02
= 0.0392

(c)
P(at least one of the engines falls)
= 1 - P(no engines falls)
= 1 - 0.9604
= 0.0396

4.
(a)
P(A|B)
= P(A∩B) / P(B)
= (1/6) / (1/4)
= 2/3

(b)
P(B|A)
= P(A∩B) / P(A)
= (1/6) / (1/3)
= 1/2

參考: 賣女孩的火柴

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