Respuesta :
Answer:
Step-by-step explanation:
Given that you have applied for two scholarships, a Merit scholarship (M) and an Athletic scholarship (A).
The probability that you receive an Athletic scholarship is 0.18
P(A) = 0.18
The probability of receiving both scholarships is 0.11.
P(AM) = 0.11
The probability of getting at least one of the scholarships is 0.3.
P(AUM) = 0.3
i.e. P(AUM) =P(A)+P(M)-P(AM) = 0.3
0.18+P(M)-0.11 = 0.3
P(M) = 0.41-0.18 = 0.23
a) the probability that you will receive a Merit scholarship=0.23
b) P(AB) not equals 0
Hence A and B are not mutually exclusive
c) P(AM) = 0.11 and P(A)*P(M) = 0.23*0.18 not equals 0.11
Hence not independent
d) P(A/M) = P(AM)/P(M) = 0.11/0.23 =0.4783
Using probability concepts, it is found that:
a) There is a 0.23 = 23% probability that you will receive a Merit scholarship.
b) Since [tex]P(A \cap M) \neq 0[/tex], events A and M are not mutually exclusive.
c) Since [tex]P(A \cap M) \neq P(A)P(M)[/tex], events A and M are not independent.
d) There is a 0.4783 = 47.83% probability of receiving the Athletic scholarship given that you have been awarded the Merit scholarship.
e) There is a 0.6111 = 61.11% probability of receiving the Merit scholarship given that you have been awarded the Athletic scholarship.
The probabilities given are:
- 0.18 probability of receiving an athletic scholarship, thus [tex]P(A) = 0.18[/tex].
- 0.11 probability of receiving both scholarships, thus [tex]P(A \cap M) = 0.11[/tex].
- 0.3 probability of receiving at least one scholarship, thus [tex]P(A \cup M) = 0.3[/tex].
Item a:
The Venn relation for the "or" probability is given by:
[tex]P(A \cup M) = P(A) + P(M) - P(A \cap M)[/tex]
We want to find P(M), thus:
[tex]0.3 = 0.18 + P(M) - 0.11[/tex]
[tex]P(M) = 0.23[/tex]
0.23 = 23% probability that you will receive a Merit scholarship.
Item b:
Since [tex]P(A \cap M) \neq 0[/tex], events A and M are not mutually exclusive.
Item c:
[tex]P(A \cap M) = 0.11[/tex]
[tex]P(A)P(M) = 0.18(0.23) = 0.0414[/tex]
Since [tex]P(A \cap M) \neq P(A)P(M)[/tex], events A and M are not independent.
Item d:
Using conditional probability, this probability is given by:
[tex]P(A|M) = \frac{P(A \cap M)}{P(M)} = \frac{0.11}{0.23} = 0.4783[/tex]
0.4783 = 47.83% probability of receiving the Athletic scholarship given that you have been awarded the Merit scholarship.
Item e:
[tex]P(M|A) = \frac{P(A \cap M)}{P(M)} = \frac{0.11}{0.18} = 0.6111[/tex]
0.6111 = 61.11% probability of receiving the Merit scholarship given that you have been awarded the Athletic scholarship.
A similar problem is given at https://brainly.com/question/14478923
