a. P( patient experience neither migraines nor weigth gain)= 0.47
b. P(Patient experiences migraines given that the patient experiences weight gain) = 0.4667
c. P(Patient experiences weight gain given that the patient experiences migraines) = 0.3783
d. Both the events are not mutually exclusive.
e. The two events are not independent.
What do you mean by conditional probability?
The possibility of an event or outcome happening contingent on the occurrence of a prior event or outcome is known as conditional probability. The probability of the prior event is multiplied by the current likelihood of the subsequent, or conditional, occurrence to determine the conditional probability.
Patient experience migraines, P(M) = 37% = 37/100 = 0.37
Patient experience weight gain, P(W) = 30% = 30/100 = 0.3
Patient experience both, P(M∩W) = 14% = 14/100 = 0.14
a. Probability of patient experience neither migraines nor weigth gain = 1 - P(M∪W)
P( patient experience neither migraines nor weigth gain) = 1 - (P(M) + P(W) - P(M∩W) = 1 - (0.37 + 0.3 - 0.14)
= 1 - (0.53)
= 0.47
Therefore, P( patient experience neither migraines nor weigth gain)= 0.47
b. Using conditional probability,
P(Patient experiences migraines given that the patient experiences weight gain) , P(M/W) = P(M∩W)/P(W) = 0.14/0.3 = 0.4667
c. P(Patient experiences weight gain given that the patient experiences migraines), P(W/M) = P(W∩M)/P(M) = 0.14/0.37 = 0.3783
d. For two events to be mutually exclusive P(M∩W) should be 0, but according to question , P(M∩W) = 0.14
Thereofre, both the events are not mutually exclusive.
e. For two events to be independent,
P(M) · P(W) = P(M∩W)
Here, P(M)· P(W) = 0.37 × 0.3 = 0.111
P(M∩W) = 0.14
Therefore, P(M)·P(W) ≠ P(M∩W)
Hence, the two events are not independent.
To learn more about the probability from the given link.
brainly.com/question/25870256
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