Find the probability that the new course is introduced.
Question: Three professors A, B and C appear in an interview for the post of Principal. Their chances of getting selected as a principal are 2/9, 4/9, 1/3. The probabilities they introduce new course in the college are 3/10, 1/2, 4/5 respectively. Find the probability that the new course is introduced.
(you are supposed to fill in the blanks for this question.)
Let A, B, C be the events that prof. A, B and C are selected as principal.
Given P(A) = 2/9 , P(B) = 4/9 , P(C) = 1/3 = 3/9
Let N be the event that New Course is introduced
P(NA) = ___, P(NB) = ___, P(NC) = 4/5
N = (A ∩ N) U (B ∩ __) U (__ ∩ N)
P(N) = (A ∩ N) + (B ∩ __) + (__ ∩ N)
= P(A) x P(NA) + P(__) x ___ + ___ x P(NC)
= ___ ___ + ___ ___ + ___ ___
= ___ + ___ + ___
= ___
***
Background knowledge/info:
1. Multiplication theorem: The probability of simultaneous occurrence of two events A and B is equal to the product of the probability of the other, given that the first one has occurred.
P(A ∩ B) = P(A) . P(BA)
P(BA) = P(A ∩ B) / P(A)
Similarly,
P(A ∩ B) = P(B) . P(AB)
P(AB) = P(A ∩ B) / P(B)
2. Independent events: The events that do NOT depend on (or affect the occurrence of) each other. The probability of one event is NOT changed by the realization or outcome of another event.
If A and B are independent events, then
P(AB) = P(AB') = P(A)
P(BA) = P(BA') = P(B)
P(A ∩ B) = P(A) x P(B)
(you are supposed to fill in the blanks for this question.)
Let A, B, C be the events that prof. A, B and C are selected as principal.
Given P(A) = 2/9 , P(B) = 4/9 , P(C) = 1/3 = 3/9
Let N be the event that New Course is introduced
P(NA) = ___, P(NB) = ___, P(NC) = 4/5
N = (A ∩ N) U (B ∩ __) U (__ ∩ N)
P(N) = (A ∩ N) + (B ∩ __) + (__ ∩ N)
= P(A) x P(NA) + P(__) x ___ + ___ x P(NC)
= ___ ___ + ___ ___ + ___ ___
= ___ + ___ + ___
= ___
***
Background knowledge/info:
1. Multiplication theorem: The probability of simultaneous occurrence of two events A and B is equal to the product of the probability of the other, given that the first one has occurred.
P(A ∩ B) = P(A) . P(BA)
P(BA) = P(A ∩ B) / P(A)
Similarly,
P(A ∩ B) = P(B) . P(AB)
P(AB) = P(A ∩ B) / P(B)
2. Independent events: The events that do NOT depend on (or affect the occurrence of) each other. The probability of one event is NOT changed by the realization or outcome of another event.
If A and B are independent events, then
P(AB) = P(AB') = P(A)
P(BA) = P(BA') = P(B)
P(A ∩ B) = P(A) x P(B)
1 Answer
Let A, B, C be the events that prof. A, B and C are selected as principal.
Given P(A) = 2/9 , P(B) = 4/9 , P(C) = 1/3 = 3/9
Let N be the event that New Course is introduced
P(NA) = 3/10, P(NB) = 1/2, P(NC) = 4/5
N = (A ∩ N) U (B ∩ N) U (C ∩ N)
P(N) = (A ∩ N) + (B ∩N) + (C ∩ N)
= P(A) x P(NA) + P(B) x P(NB) + P(C) x P(NC)
= 2/9 . 3/10+ 4/9. 1/2 + 3/9.4/5
= 6/90 + 2/9+ 12/45=6/90 + 20/90+ 24/90
= 50/90=5/9.
Daniel90
436

Thank you so much, Daniel!!!
Join Matchmaticians Affiliate Marketing
Program to earn up to a 50% commission on every question that your affiliated users ask or answer.
 1 Answer
 173 views
 Pro Bono
Related Questions
 How do you calculate per 1,000? And how do you compensate for additional variables?
 applied probability
 Normal distribution & Probability
 Finding the probability that a roughly normal distributed will have the highest value among multiple curves
 Wiener process probability
 2 Player Limited Information Game
 Please check if my answers are correct  statistic, probability
 A question in probability theory