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Galina-37 [17]
3 years ago
6

You want to go to graduate school, so you ask your math professor, Dr. Emmy Noether, for a letter of recommendation. You estimat

e that there is a 80% chance that you will get into a graduate program if you receive a strong recommendation, a 60% chance that you will get into a graduate program if you receive a moderately good recommendation, and 5% chance that you will get into a graduate program if you receive a weak recommendation. Furthermore, you estimate that the probabilities that a recommendation will be strong, moderately good, and weak are 0.7, 0.2, and 0.1, respectively. Based on these estimates, what is the probability that you will get into a graduate program. Given that you did receive an offer to attend a graduate program, what is the probability that you received a strong recommendation? Suppose you didn't receive an offer to attend a graduate program. Given that, what is the probability that you received a moderately good recommendation?
Mathematics
1 answer:
den301095 [7]3 years ago
3 0

Answer:

a

  P(G) =  0.69

b

  P(S | G) = 0.81

c

  P(M|G') =  0.26

Step-by-step explanation:

From the question we are told the

   The probability of getting into getting into graduated school if you receive a strong recommendation is  P(G |S) = 0.80

   The probability of getting into getting into graduated school if you receive a moderately good recommendation is  P(G| M) =  0.60

   The probability of getting into getting into graduated school if you receive a weak recommendation is  P(G|W) =  0.05

   The probability of getting a strong recommendation is  P(S) =  0.7

     The  probability of receiving a moderately good recommendation is P(M) =  0.2

       The probability of receiving a weak recommendation is P(W) =  0.1

      Generally  the probability that you will get into a graduate program is mathematically represented as

     P(G) =  P(S) *  P(G|S) + P(M) *  P(G|M) + P(W) *  P(G|W)

=>   P(G) =  0.7 * 0.8 +  0.2 *  0.6 + 0.1 *  0.05

=>   P(G) =  0.69

Generally  given that you did receive an offer to attend a graduate program, what is the probability that you received a strong recommendation is mathematically represented as

      P( S|G) =  \frac{ P(S) *  P(G|S)}{ P(G)}

=>    P(S|G) =  \frac{ 0.7 * 0.8 }{0.69}

=>     P(S | G) = 0.81

Generally given that you didn't receive an offer to attend a graduate program  the probability that you received a moderately good recommendation is mathematically represented as

        P(M|G') =  \frac{ P(M) *  (1- P(G|M))}{(1 - P(G))}

         P(M| G') =  \frac{ 0.2 *  (1- 0.6)}{ (1 - 0.69)}

         P(M|G') =  0.26

 

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