Quantitative methods 請幫忙睇下我做得對嗎?

It is estimated that the probability that the Hong Kong prime rate will drop below 6% this month is 0.6. If this happens the probability that the Hang Seng Index will reach 20,000 is estimattied to be 0.7. If the prime rate stays at 6% or above, the probability that the Hang Seng Index will reach 20,000 is estimated at only 0.4. Find:

更新1:

(a) p(prime rate under 6% and Hang Send Index reaches 20,000). (b) p(prime rate under 6% and Hang Send Index under 20,000). (c) p(prime rate 6% or more and Hang Send Index reaches 20,000). (d) p(prime rate 6% or more and Hang Send Index under 20,000). (e) p(Hang Send Index reaches 20,000).

更新2:

Let S represpresent all probability Let A represpresent prime rate under 6% Let B represpresent Hang Seng Index reaches 20,000 P(A) = 0.6 P(not A) = 1- P(A) = 0.4 P(B|A) = 0.7 P(not B|A) = 0.3 P(B| not A) = 0.4 P(not B| not A) = 0.6

更新3:

(a) P(A and B) = P(B|A) x P(A) = 0.7 x 0.6 = 0.42 (b) P(A and not B) = P(not B|A) x P(A) = 0.3 x 0.6 = 0.18 (c) P(not A and B) = P(B| not A) x P(not A) = 0.4 x 0.4 = 0.16 (d) P(not A and not B) = P(not B| not A) x P(not A) = 0.6 x 0.4 = 0.24

更新4:

(e) P(A or B) = 1 - P(not A and not B) = 1- 0.24 = 0.76 P(A or B) = P(A) + P(B) - P(A and B) P(B) = P(A or B) - P(A) + P(A and B) = 0.76 - 0.6 + 0.42 = 0.58

Quantitative methods 請幫忙睇下我做得對嗎?

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