1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
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

 

You might be interested in
A piece of wood is divided into two pieces in the ratio of 2:5. One piece is 10 cm long so how long is the other piece?
klio [65]

Answer:

The length of the pother piece of the wood is 25 cm.

Step-by-step explanation:

Let the length of a piece of wood is x such that the ratio of two pieces is 2:5. Two pieces are 2x and 5 x

Length of the first piece is 10 cm. It means, 2x = 10 i.e. x = 5

We have considered that the length of other piece is 5x. It means 5×5 = 25 cm.

Hence, the length of the pother piece of the wood is 25 cm

8 0
3 years ago
68
Scilla [17]
Can you repost this with a picture please ?
7 0
2 years ago
Molly is baking for the moms and muffins event at her school. She will bake 4 batches of banana muffins. She needs 1 3/4 cups of
garri49 [273]
Part A = She incorrectly add 1 (4/4) with 3/4, so instead of getting 7/4 she got 8/4.
Part B=She needs 28/4 (7) cups for 4 batches because 4/1x7/4=28/4.
7 0
2 years ago
Read 2 more answers
13. which inequality has the following graphed solution?
mafiozo [28]
B. You have to solve for X, and graph using whatever is less than or greater than. 4x + 12 < 4 to 4x < -8 to x < -2.
5 0
2 years ago
A survey asks 48 randomly chosen students if they plan to buy a school newspaper this week. Of the 48 surveyed,32 plant to buy a
spayn [35]
The answer is 540 because 32/48 is 2/3 and 360/540 equals 2/3
4 0
3 years ago
Other questions:
  • For what value of a does 9 = (StartFraction 1 Over 27 EndFraction) Superscript a + 3?
    15·1 answer
  • What is the perimeter of this polygon
    13·2 answers
  • Carla has two lengths of ribbon. One ribbon is 2 ft. The other ribbon is 30 inches. Which ribbon is longer. Explain.
    5·1 answer
  • Decimals between 4.2 and 5.4 with an interval of 0.3 between each pair of decimals
    13·1 answer
  • On a P nombre apartin à New <br> et P divise x+y et x-y <br> déduire que P divise x et y
    5·1 answer
  • Subtract 39 from 42, and then subtract that difference from 26. Which expression means the same as these words?
    15·1 answer
  • The game of checkers is played on a square board. If the length of one side of the board is 4^2 inches, what is the area of the
    9·1 answer
  • PLEASEEE HELP PLEASEEE!!!!
    10·1 answer
  • ILL BRAINLIEST YOU PLEASE HELP WITH THIS
    14·1 answer
  • Pls help me thank you
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!