(a)Therefore, the probability that the order is made at restaurant K and being sent after 15 minutes is 0.364.

(b) The probability that the order is made at restaurant M given that it is sent in 15 minutes is 0.543.

(c) P(K | 33 minutes) = P(33 minutes | K) x P(K) / P(33 minutes)

= 0.09 x 0.4 / 0.126

= 0.286

Penjelasan dengan langkah-langkah:

(a) The probability that the order is made at restaurant K and being sent after 15 minutes is given by the product of the probabilities along the path K-0.4-0.91: P(K and 15 minutes) = P(K) x P(15 minutes | K) = 0.4 x 0.91 = 0.364

(b)P(M | 15 minutes) = P(M and 15 minutes) / P(15 minutes) To find P(M and 15 minutes), we add the probabilities along the path M-0.5-0.94:

P(M and 15 minutes) = P(M) x P(15 minutes | M) = 0.5 x 0.94 = 0.47

To find P(15 minutes), we add the probabilities of all the paths that lead to 15 minutes:

P(15 minutes) = P(K) x P(15 minutes | K) + P(M) x P(15 minutes | M) + P(P) x P(15 minutes | P)

= 0.4 x 0.91 + 0.5 x 0.94 + 0.1 x 0.8

= 0.865

Therefore, P(M | 15 minutes) = P(M and 15 minutes) / P(15 minutes) = 0.47 / 0.865 = 0.543

(c)To find the probability that Jimin ordered from each of these restaurants, we need to use Bayes' theorem:

P(K | 33 minutes) = P(33 minutes | K) x P(K) / P(33 minutes)

To find P(33 minutes | K), we subtract the probability of being sent in 15 minutes from 1:

P(33 minutes | K) = 1 - P(15 minutes | K) = 1 - 0.91 = 0.09

To find P(33 minutes), we add the probabilities of all the paths that lead to 33 minutes:

P(33 minutes) = P(K) x P(33 minutes | K) + P(M) x P(33 minutes | M) + P(P) x P(33 minutes | P)

= 0.4 x 0.09 + 0.5 x 0.06 + 0.1 x 0.8

= 0.126

Therefore, P(K | 33 minutes) = P(33 minutes | K) x P(K) / P(33 minutes)

= 0.09 x 0.4 / 0.126

= 0.286

Pelajari lebih lanjut

Pelajari lebih lanjut materi tentang probability: yomemimo.com/tugas/15910542

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