Let E and F be two events in S with P(E) = 0.7, P(F) = 0.26, and P(E ∩ F) = 0.16. Find P(EC ∩ F) and P(EC ∩ FC). P(EC ∩ F)     P(EC ∩ FC)

Q: Let A and B be two events such that P(A|B)=P(A|BC), where BC is the complement of B), and 0 < P(B) <…

A: We use the conditional probability formula to prove that A and B are independent.…

Q: Let E and F be two events in S with P(E) = 0.27, P(F) = 0.66, and P(E ∪ F) = 0.82. Find P(E ∩ F) and…

A: We have given that, Let E and F be two events in S (Sample space). P(E)=0.27, P(F)=0.66, P(E∪F)=0.82

Q: 2. Let A and B be two events with P(A) = and P(B) = . Show that %3D (a) P(AU B) > 3/4 (b) 를<P(An B)…

A: Event: In probability theory, an event is an outcome or a set of outcomes of a random experiment to…

Q: 4. Show that an event A is independent of itself iff P(A) is either 0 or 1.

A: Proof: PA=PA∩A=PAPA  Since A is independent itself.⇒PA1-PA=0PA=1  Since P(A)&gt;0

Q: Consider two events A and B. Suppose P (A ∪ B) = 0.7 and P (A ∪ B′) = 0.9. Find P (A) (a Venn…

A: The given data for events A and B is(A  B) = 0.7 and P (A  B′) = 0.9

Q: let A and B be two events in an outcome space M such that M = A U B, P (A) = 0.65 and P (B) = 0.75.…

A:

Q: Suppose that the events A, B, and C are independents, where P(A)= 1/2, P(B)=1/3, and P(C)= 1/4. What…

A: Given that A, B, and C are independents. So,…

Q: Let E, F and G be three events in S with P(E) = 0.43, P(F) = 0.61, P(G) = 0.58, P(E ∩ F) = 0.29, P(E…

A: Let A and B be two events then, according to the De Morgan's law, P(Ac ∪ Bc) = P(A ∩ B)c ⇒P(Ac ∪ Bc)…

Q: Let A and B be events with P(A) = 0.8, P (B) = 0.4, and P (B|A) = 0.2. Fins P(A and B).

A: There are two events A and B given with probabilities such as PA=0.8, PB=0.4, and PB|A=0.2.

Q: Let E, F and G be three events in S with P(E) = 0.4, P(F) = 0.5, P(G) = 0.29, P(E ∩ F) = 0.28, P(E ∩…

A: Given DataP(E) = 0.4, P(F) = 0.5,P(G) = 0.29, P (E ∩ F) = 0.28, P(E ∩ G) = 0.11, P(F ∩ G) = 0.14,…

Q: Let A and B be events such that: P(A) = 0.5, P(B) = 0.6, P(A∩B) = .4a. P(A ∪ B) =b. P (A|B) =c.…

A: It is given that:

Q: Let E and F be two events in S with P(E) = 0.39, P(F) = 0.4, and P(E ∩ F) = 0.22. Find P(EC ∩ F) and…

A: To compute the probabilities of the required events , using addition and complementation laws

Q: If A and B are mutually exclusive events then O a. 1- P(AN B) = P(A) + P(B) %3D | O b. P(AU B) =…

A: Mutually exclusive events: Two events A and B are said to be mutually exclusion if there are no…

Q: Theorem 3.16. For any three events A, B and C, Р (AnB IC)+ P (AnBIC)- Р (AI C)

A:

Q: Show that if A and B, (n = 1,2,3, . -) are events, then An (U Bn) = U (AN Bm)

A:

Q: Exercise 1. Let A and B be independent events with P(A) = 0.7 and P(B) = 0.2. Compute (a) P(An B),…

A: Given problem Given that

Q: Example 17. If A and B are two events such that P(A) = P(B) = and Р(A u B) %3 2 A Find P B 1/4 1/3

A: Solution:

Q: A,B, and C are mutually exclusive events such that P(A) = 0.2,P(B) = 0.6, and P(C) = 0.1. Find P(A…

A: The formula for P(A or B or C) is given below:

Q: Suppose that A and B are events such that P(A) = 1/3, P(B) = 1/2 and P(A ∪ B) = 5/6. Find (a) P(A ∩…

A:

Q: Let E and F be two events in S with P(E) = 0.45, P(F) = 0.63, and P(E ∪ F) = 0.87. Find P(E ∩ F) and…

A: Formula:For 2 events A and B, P (A ⋃ B) = P (A) + P (B) – P (A ∩ B).

Q: 3. Let C and D be events with P(C) = 0.1, P(D) = 0.6, and P(C U D) Are C and D independent? Explain.

A:

Q: 3. Two events A and B are such that P (A) = 0.6, P (B) = 0.4 and P(A/B) = 0.2 Find a) P(ANB) b)…

A: it is given that  P(A) = 0.6 P(B) = 0.4 P( A/B ) = 0.2   Note: According to Bartleby expert…

Q: you say about P(B)?

A:

Q: Let A and B be any two events defined on S. suppose that p(A)=0.2, p(B)=0.7, and p(A and B)=0.3, the…

A: It is given that, p(A) =0.2 p(B) =0.7 and p(A and B) =0.3

Q: Theorem 3-18. If A and B are independent events, then (i) A and B (ii) A and B (iii) A and B, are…

A:

Q: Let E, F and G be three events in S with P(E) = 0.37, P(F) = 0.56, P(G) = 0.54, P(E ∩ F) = 0.18, P(E…

A: De-Morgan law:Let E, F and G be three events then,

Q: Suppose Q and R are independent events. P(Q) = 0.25 and P(Q and R) = 0.1. Find P(R):

A: Given that  Q and R are independent events. P(Q) = 0.25 and P(Q and R) = 0.1

Q: If A and B are independent events, then ... None of the above OP(AUB)=P(A)×P(B) OP(A U B) = 1OP(An…

A: If events A and B are independent, it means that the occurrence or non-occurrence of one event does…

Q: If P(A A. B. C. D. B) = 0 A and B are independent events. P(A) + P(B) = 1 A and B are mutually…

A: given data  P(A∩B) = 0 we have to find correct statement from given options.

Q: Let E, F and G be three events in S with P(E) = 0.58, P(F) = 0.34, P(G) = 0.33, P(E ∩ F) = 0.2, P(E…

A: Consider E, F and G be three independent events in sample space, S.

Q: Let A, B, be two independent events such that P(A) = P(B) = 0.3 then P(A UBC) =

A: Given that PA=PB=0.3 A and B are independent events. Hence, P(A and B)=P(A)*P(B)=0.3*0.3=0.09

Q: Let E, F and G be three events in S with P(E) = 0.4, P(F) = 0.5, P(G) = 0.29, P(E ∩ F) = 0.28, P(E ∩…

A: The provided information is:

Q: If E and F are two disjoint events in S with P(E) = 0.23 and P(F) = 0.6, find P(E ∪ F), P(EC), P(E ∩…

A: From the question, it is given that E and F are two disjoint events in S that is both events are…

Q: If P(E) = 0.2, P(F) = 0.3, and E and F are independent events, find P(E and F). 1) 0.06 2) 0.08 3)…

A: Given : p ( E ) = 0.2 p ( F) = 0.3