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

a

b

c

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  

   The probability of getting into getting into graduated school if you receive a moderately good recommendation is  

   The probability of getting into getting into graduated school if you receive a weak recommendation is  

   The probability of getting a strong recommendation is  

     The  probability of receiving a moderately good recommendation is

       The probability of receiving a weak recommendation is

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

=>  

=>  

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

=>    

=>    

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