I) P(A') = 1- P(A) = 1- 1/3 = 2/3
ii) P(A U B) = P(A)+ P(B)- P(A intersection B)
= 1/3 + 1/4 - 1/5
= (20+15-12)/60
= 23/60
III) P( A' intersection B)= P(B) - P(A intersection B)
= 1/4 - 1/5
= 1/20
iv) P(A intersection B') = P(A) - P ( A intersection B)
= 1/3-1/5
= 2/15
v) P(A' intersection B') = P( A U B)'
= 1-P(AUB)
= 1- 23/60
= 37/60
vi) P(A' U B) = P(A') + P(B) - P(A' intersection B)
= 2/3 + 1/4- 1/20
=( 40+ 15- 3)/60
= 52/60
vii) P(A'- B)= 1- P(A U B)
= 1- 23/60
= 37/60
viii) P(A'-B') = P(A')- P(A' intersection B')
= 2/3 - 37/60
= (40 - 37)/ 60
= 3/60
(1) If A and B are two events suchthat PA)1.P(B) -and P(AnB) -.Determine the following: 3...
2. Let A and B be events in a sample space such that P(A) -0.5. P(ANB) -0.3 and PLAUB)=0.8. Calculate: 1) P(AB): ii) P(BA): iii) PIBIA B): be independent of A and such that B and Care Let the event C in mutually exclusive. Calculate: iv) P(AC); v) PIANBNC). (8 Marks)
Problem 3. Show the formula P((An B)U(A n B))- P(A) +P(B)-2P(AnB), which givgs the probability that exactly one of the events A and B will occur. [Compare with the formula P(AU B) P(A) P(B) - P(AnB), which gives the probability that at least one of the events A and B will occur.]
1 Let A and B be independent events with P(A) and P(B) = FICE Find P(ANB) and P(AUB). 8 P(ANB) = P(AUB) =
Match the rules to their correct notation: >P(AnB) P(A) (BIA) 1. Addition Rule 2. Multiplication Rule P(A) Independent events Multiplication Rule - Dependent events 3. P(AnB)P(A) P(B) PAUB)PA)P(B)(AnB) 4. Conditional Probability
Let A and B be events with probabilities P(A)-3/4 and P(B)-1/3 (a) Show that 12 3' (b) Let P(AnB) - find PA n Bc).
8. Let P(A) P(B) - 1/3 and P(AnB) 1/10. Find the following: (b) P(AUB') () P(Bn A (d) PA UB)
Help please! Suppose two events A and B are two independent events with P(A) > P(B) and P(AU B) = 0.626 and PAn B)-0.144, determine the values of P(A) and P(B). 9.
Consider the following system at equilibrium. N2(g) + 3 H2 (g) 2 NH3(g) + 92.24 kJ <--> Which response includes all of the following that will shift the equilibriu to the right, and no others? I. increasing the temperature III. increasing the pressure II. decreasing the temperature IV. decreasing the pressure VI. adding some NH3 V. removing some NH3 VII. removing some N2 VIII. adding some N2 a) I, IV, VI, and VII c) I, VI, and VII e) II,...
Two events A and B are such that P(A)2, P(B).3, and P(AUB) -4. Find following: a P(An B) b P(AUB) d P(AB) If A and B are independent events with P(A)and P(B) .2, find the following: a P(AUB) b PAnB) c P(AU B)
Suppose two events A and B are two independent events with P(A) > P(B) and P(A U B) = 0.626 and PA กั B) 0.144, determine the values of P(A) and P(B).