P(A) - I P(B) =0 P(A and B) =] P(A or B) = P(A)+ P(B) P(A and B

Q: Given P(A and B) = 0.22, P(B) = 0.75, P(B|A) = 0.84, what is P(A)?

A: Given information- P(B) = 0.75 P(A∩B) = 0.22 P(B|A) = 0.84 P(B/A) is given by-

Q: If P(B) = 1/4 and P(A|B) = 1/2, what is P(A^ B)?

A: P(B¯) = 1/4P(A|B) = 1/2We have to determine P(A∩B).

Q: Given P(A and B) = 0.37, P(B) = 0.57, P(B|A) = 0.91, what is P(A)?

A: We have to find given probability.

Q: P(A)=0.7 P(B)=0.4 P(A or B)=0.3 Find P(A and B)

A: Solution: From the given information, P (A)=0.7, P(B)=0.4 and P(A or B)=0.3.

Q: (g) P(A)– P (B) (h) P(AnB) (f) P(A)n P(B) (i) P(A)× P(B)

A:

Q: If P(A) = 0.7, P(B) =0.2, and A and B are mutually exclusive, find P (A or B). P(4 or B) = D

A:

Q: = 0.40, what is P(A)?

A: Independent event- two events ( suppose A and B) are called to be independent events if the outcome…

Q: Given P(A) = 0.78, P(B) = 0.87, and P(B|A) = 0.44, what is P(A and B)?

A: Given :  P(A) = 0.78 P(B) = 0.87 P(B|A) = 0.44

Q: P(A|B) = 0.2, P(A) = 0.5, P(B) = 0.45                    Find P(A U B)

A:

Q: ■ P(a)=P(a) (0.9) + P(b) (0.1) + P(c) (0.3) ■ P(b)=P(a) (0.05) + P(b) (0.8) + P(c) (0) ■ P(c)=P(a)…

A: Given data, Pa=Pa0.9+Pb0.1+Pc0.3Pb=Pa0.05+Pb0.8+Pc0Pc=Pa0.05+Pb0.1+Pc0.7

Q: Given P(A) = 0.94, P(B) = 0.98, P(B|A) = 0.52, what is P(A and B)?

A:

Q: Given P(A) = 0.01, P(B) = 0.88 , and P(B|A)=0.34 , what is P(A and B)?

A: Given: P(A)=0.01P(B)=0.88P(BA)=0.34 The objective is to find the probability of P(A∩B).

Q: P(A) = 0.25, P(B) = 0.65, P(AU B)= 0.8 Find a) P(A|B)        b) P(B|A)

A: First we need to find P(AnB). P(AnB) = P(A)+P(B)-P(AUB) = 0.25+0.65-0.8 = 0.1

Q: If P(A) = 0.4, P(B) = 0.9, \ and P(An B) = 0.3, \ then (a) P(A|B) = \ and (b) P(B|A) =

A: We have to find given probability...

Q: Suppose that P(A) = 0.12, P(B) = 0.40 and P(B|A) = 0.60. (a) What is P(A and B)? (b) What is P(A…

A:

Q: To find out whether a new serum will arrest leukemia, 11 mice, all with an advanced stage of the…

A: The null and alternative hypotheses are stated as follows:

Q: 12. Find a normal vector n and an equation for the planes in Figures & (A)-(C).

A:

Q: Given P(A) = 0.86, P(B) = 0.77, P(B|A) = 0.37, what is P(A and B)?

A: Let A and B are two events. The known probabilities are, Using the conditional probability formula,…

Q: Given P(A) = 0.22, P(B) = 0.24, and P(B|A) = 0.21, are A and B independent or dependent?

A: We know,  P(B/A) = P(A∩B)/P(A)     P(A∩B) = P(A) P(B) Events A and B are independent if the equation…

Q: Given P(A) = 0.16, P(B) = 0.88, P(B|A) = 0.25, what is P(A and B)?

A: Given , P(A) = 0.16, P(B) = 0.88, P(B|A) = 0.25

Q: iven P(A) = 0.25, P(B) = 0.28, and P(B|A) = 0.28, are A and B independent or dependent?

A:

Q: Given P(B) = 0.47, P(A and B) = 0.21, P(A or B) = 0.40, what is P(A)?

A: P(B) = 0.47 P(A and B) = 0.21 P(A or B) = 0.40

Q: (b) 6 + 7 + 8 + 9 + ... + k

A: (b) Given that 6+7+8+9+...+k The objective is to find the sum. The formula for sum of numbers are,…

Q: Given P(A) = 0.21, P(B) = 0.24, and P(B|A) = 0.24, are A and B independent or dependent?

A:

Q: P(A) = 0.13, P(B) = 0.47, P (A ∩ B) = 0.05 Find a) P(A|B).   b) P(B|A)

A: P(A) = 0.13, P(B) = 0.47, P (A ∩ B) = 0.05   We know :

Q: P(A) = 0.5, P(B) = 0.3, P(A ∩ B)= 0.1 a) Find P(A given B).   b) P(B|A)

A: As per given by the question, there are P(A) = 0.5, P(B) = 0.3,and P(A ∩ B)= 0.1., then find PA…

Q: P(A) = 0.2, P(B) = 0.6, P(AUB)= 0.7 Find a) P(A|B)  b) P(B|A)

A:

Q: P(A ∪ B) = 0.9, P(B) = 0.7, P(A ∩ B) = 0.5. Find P(A).

A: A detailed solution is given below

Q: GivenP(A) = 0.4,  P(B) = 0.5, P(A | B) = 0.3 Compute  P(A and B) Compute P(A or B).

A: P(A) = 0.4, P(B) = 0.5, P(A|B) = 0.3

Q: SAT scores are normally distributed with mean = 1000 and standard deviation σ = 200. 15) Take a…

A: SAT scores are normally distributed with mean and standard deviation :mean = 1000standard deviation…

Q: P(a)=7/10 p(b)=3/5 p(a and b)=? P(a)=13/20 p(a and b)=13/50 p(b)

A: P(a).P(b)=p(a and b)

Magnitude

A vector is an element with both direction and magnitude. A vector is represented using an arrow, where the arrow represents the direction of the vector and its length is represented using the magnitude. The set of vectors in space is known as vector space. The vectors can be added, subtracted, multiplied, and divided in a vector space. The image below shows a vector AB.