7. Given P(A) = 1/3 and P(B) = 1/2 and P(A U B) = 2/3 • (d) Find P(BIA) • (e) Are events A & B Independent? (f) Are events A & B Mutually exclusive?

Q: Independence). (i) Recall that given events A, B,C, we have that P(AUBUC) = P(A)+ P(B)+ P(C) – P(An…

A: Hello! As you have posted 3 different questions, we are answering the first question. In case you…

Q: If the joint probability of the random variables X and Y is ! for 0<y< 4r < 4 S(z. y) = 0 lsewhere,…

A: Given the joint probability function- f(x,y)=12for 0&lt;y&lt;4x&lt;40elsewhere We need to find the…

Q: 5 boys & 5 girls sit in a row randomly, then (A) Probability that 5 girls sit together = 56 10…

A: Probability = favorable outcomes /total outcomes According to guidelines, we can solve only one…

Q: For two events, M and N, P(M)=0.4, P(N|M) = 0.7, and P(N|M')=0.2. Find P(MIN'). P(MIN') = (Simplify…

A: For two events M  and N, the given probabilities are as follows, P(M)=0.4P(N|M)=0.7P(N|M')=0.2 Since…

Q: 4. Suppose that the events A and B are mutually exclusive with P(A) Let A' denote the complement of…

A: given data mutually exclusive eventsP(A) = 0.4P(B) = 0.4P(A'∩B) = ?

Q: if P(A)= 0.70 , P(B)= 0.60 P(ANB)=0.50 Then P(A/BC) =

A: Given that PA=0.70PB=0.60PA∩B=0.50

Q: (1) Let X be a random variable with p.d.f. ke 2x f(x) ={ 0 <x<0 , then o.w (a) k=3 (b) k=2 (c) k =-…

A: Reviewing information, X is a r.v. with pdf, f(x)=k·e-2x                                   ;…

Q: If E and F are two independent events, such that P (E ∩ F ) = 1/6 , P (E' ∩ F' ) = 1/3 and (P (E) −…

A:

Q: (3) Let X be a random variable with p.df 12(3x+ 0<x<1 15 , then P(0<x< 0.5) is o.w 7 (d) 7 (a) 60…

A:

Q: (8) X and Y are independent events. P(X)=0.3; P(Y)=0.4. Find (d) P(X or Y) (9) Repeat the previous…

A: " Or" indicates union.

Q: When a man observed a sobriety checkpoint conducted by a police department, he saw 671 drivers were…

A: According to the given information, we have Total number of drivers = 671 Number of drivers that…

Q: Suppose f(x), the pmf for a discrete random variable X is given in the table below: 10 15 f (x) |…

A:

Q: 13. If {Bk} are events such that >P(Bk) > n – 1, k=1 then P Bx) > 0. k=1

A:

Q: 6x) 0<x<1 S(x)%=D , then p(x<1) is (a) 1 (b) 2 (c) 3 (d) 4 (c) None of these

A: It is an important part of statistics. It is widely used.

Q: Ifa is a binomial random variable, compute P(x) for each of the following cases: (a) P(x ≤ 4), n =…

A: We know that, Probability mass function for binomial distribution is, P(X= x) = nCx*(p)x*(1-p)n-x…

Q: find P( X' ∩ Y)

A: Here given x and y mutually exclusive

Q: For independent events A and B , P(A)=0.80 and P(B)=0.20, Find P(A∩B')   16/25   1/4   4/25…

A: Solution: From the given information, P(A) = 0.80 and P(B) = 0.20.

Q: Consider two events A and B such that P(A) 8' - P(A/B) 1 and P(B/A) 4 1 Examine th following…

A:

Q: 18. Suppose P(A) = 0.3 and P(AUB) = 0.5. Find P(B) under each of the following additional…

A:

Q: 3. The following table lists the probability function of the discrete variables (X, Y). Known that…

A:

Q: 6. A random variable Z has the following probability function, - 1 Z : P(Z): Find (i) the value of…

A:

Q: Q2 (30P) a) Probability function of X discrete random variable: P(x) = { x = 1,2, 3, . .,10 in other…

A: Hello. Since your question has multiple sub-parts, we will solve first three sub-parts for you. If…

Q: Suppose an event E and its complement E then P(E) +P(E) = 1 P(E) +P(E) =0 P(E) - P(E) =1 P(E) P(E)…

A:

Q: 4. Suppose two events E and F satisfy P(E)= 0.3, P(F) = 0.5 and P(E' F) = 0.3. (a) Compute P(En F).…

A: The question is about is probability Given : P ( E ) = 0.3  P ( F ) = 0.5 P ( E' ∩  F' ) = 0.3   To…

Q: Problem 1) For any two events A and B with P(B) + 0, prove that P(A| B) + P(A'| B) = 1.

A:

Q: 1.4-3. Let A and B be independent events with P(A) = 1/4 and P(B) = 2/3. Compute (a) P(A n B), (b)…

A: A and B are independent eventsP(A)=P(B)=

Q: (d) If we define the events A and B by: A = {(X,Y):2(Y – X) > Y + X} Determine P(Ān B).

A: To find the probability of the said event please repost the question with the respective probability…

Q: 3. Consider tw o evénts A and B such that Pr(A)= 1/3 and Pr(B)= 1,2. Determine the value of Pr(B 0A)…

A: Given PrA=13 and PrB=12 and A and B are disjoint, that means PrA∩B=PrA×PrB…

Q: If A and B are two events and P(A) = 0.60, P(B) = 0.30 and P(A UB) = 0.80, find: .... d) P(A' n B')…

A: We have to find given probability.

Q: m 2 and P(D) = 3 Find 10 Events C and D are mutually exclusive such that, P(C) = (a) P(C') (b)…

A: Given P(C) = 25  and  P(D) = 310

Q: 1. Determine the requested probabilities. -2 -1 1. f(x) 0.2 0.1 0.4 0.2 0.1 a) P(xs 2) b) P(x > -2)…

A: From the given table Find the probabilities

Q: If A & B are two events and p(B) ≠ 1, prove that p(A/B') = [p(A) - p(A∩B)/[1 - p(B) where B'…

A: We have, two events A and B thus,  P(A|B')=P(A∩B')P(B')          ......(1)We know that,…

Q: Given X and Y are two events. LetP(M) = 0.49, P(N) = 0.44, P(MN) = 0.17 Find the value of…

A: M,N are two events.P(M)=0.49P(N)=0.44P()= 0.17we need to find P(M/N')