Solution:
Given that,
P ( A / B ) = P (A )
P ( A ) = 0.4
P ( B ) = 0.5
a) P ( A B
) = P ( A ) * P ( B )
= 0.4 * 0.5
= 0.20
P ( A B
) = 0.20
b ) P ( A " B
) = P ( B ) - P (A )
= 0.5 - 0.4
= 0.1
P ( A " B
) = 0.1
[Q1] Suppose that PAlB) 04 and P(B0.5. Determine the following (a) P(AnB) (b) PA'nB)
(1) If A and B are two events suchthat PA)1.P(B) -and P(AnB) -.Determine the following: 3 i) P(AU B) v) PCA'U B) ii) P(A'n B) vi) P(A'- B) iv) P(AnB') viii) P(A'-B')
. Det IQ11 Suppose that P(AB) 04 (a) PAn B) (b) P(A'nB) and P(B) 0.5, Determine the following
2) Suppose A and B are independent events, then() is incorrect. PCAIB) P(A) O P(AnB) P(A)P(B) P(AUB)-P(A)+P(B) 0:(AIB) = P(A)
2-142. Suppose that P(A1 B) Determine P(BIA). : 0.6, P(A)-04, and P(B)-0.3. / 2-143. Suppose that P(AIB)=0.5,PCAI B)-0.1, and P(B) 0.7. Determine P(BIA).
Suppose that P(A)0.5, P(B)0.2, P(C) 0.3, P(AnB) 0.1 and P(AnC) 0.1. Compute the following: (a) (2 points) P(AUB) b) (6 points) P(A UC) (c) (4 points) Are the events A and B independent? What about A and C? (d) (8 points) If the sets B and C are mutually exclusive sets, what is P(A U B U C)?
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) =
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)
"the following formula: P(A|B)= P(AnB) / P(A) represents " Addition Rule Conditional probability Multiplication Rule Independence
(1) Suppose that A and B are events with P[A] = 0.4 and P[B] = 0.7. Show that 0.1 < PAB < 0.4. Justify your answer clearly. P(ANB) - PCA) PCB) = 0.4.0.7 = 0.28 with 0.15 0.28 <0.4 PLA) occuring 04 P(B) occuring 0.7 P of both events occuring at the same time should be = 0.28 which is in Ran 0,4 1028 0.7 2/10
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.]