2.1 Express the following points in Cartesian coordinates: (a) P(1, 60°, 2) (b) Q(2, 90°, –4) (c) R(, 45°, 210°) ( d) T( 4, π/2, π/6)

Q: Suppose P(A) = 0.57, P(B) = 0.20, and P(AM B)= 0.05. What is P(A| BC?

A: A and B with probabilities P(A)= 0.57 and P(B)= 0.20 P(A ⋂ B)= 0.05To find the probabilit P(A|Bc)

Q: P(A)=0.45, P(B)=0.58, and P(B|A)= 0.05. What is P(A and B)?

A: Given that  P(A)=0.45, P(B)=0.58, and P(B|A)= 0.05

Q: Given P(A) = 0.78, P(B) = 0.45, and P(B|A) = 0.97, what is P(A and B)?

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Q: If P(A or B) = 0.7 and P(A) = 0.44, and P(A and B) = 0.22, determine P(B)

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Q: Suppose P(A) = 0.48 and P(B) = 0.62. Can A and B be mutually exclusive? Why or why not.

A: We know that, mutually exclusive events are  events which can not happen at the same time.

Q: P(A U B) = 0.9, P(B) = 0.8, P(A n B) = 0.5. Find P(A). %D

A: We have given that,  P(A∪B) = 0.9, P(B) = 0.8 and P(A∩ B) = 0.5 Then,  We will find P(A) = ?

Q: Given P(A) = 0.03, P(B) = 0.42, P(B|A) = 0.28, what is P(A and B)

A: GivenP(A)=0.03P(B)=0.42P(B|A)=0.28

Q: Given P(A) = 0.06, P(B) = 0.69, P(B|A) = 0.77, what is P(A and B)?

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Q: Suppose P(B)=0.22, P(A and B)=0.125, and A and B are independent. Find P(Ac) Select one: A. 0.57 B.…

A: Given Information:PB=0.22PA and B=0.125A and B are independent.To find PAc

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: If P(B) = 0.3, P(A or B)= .06, and P(A and B)= .2, find P(A)

A: From the properties of probability, for any two events A and B we have

Q: Given P(A) = 0.39, P(B) = 0.95, and P(B|A) = 0.07, what is P(A and B)?

A: Given :  P(A) = 0.39 P(B) = 0.95 P(B|A) = 0.07

Q: P(A)=0.39P(A)=0.39, P(B)=0.36P(B)=0.36 and P(AandB)=0.25P(AandB)=0.25.P(B∣notA)=

A: It is given that, P(A)=0.39, P(B)=0.36 and P(A and B)=0.25.Let AC be the complement od the event A.…

Q: If P(A) = 0.5 and P(B) = 0.80, then P(A or B) must be 0.95.   TRUE or FALSE

A: From the provided information, P (A) = 0.5 and P (B) = 0.80

Q: Let P(A)=P(A)= 0.282.   Find P(A¯¯¯¯)P(A¯). Do not round your answer.

A: From the provided information, The probability of event A, P (A) = 0.282

Q: If P(A) = 0.35, P(B) = 0.45, and P(A and B) = 0.25, then P(A|B) is:     1.4     1.8     0.714…

A: P(A)=0.35 P(B)=0.45 P(A and B)=0.25   P(A/B)=P(A and B)P(A)=0.250.35=0.714

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: Does each of the following series converge or diverge? Why? Show all your work and MUST include the…

A: To determine whether the series ∑n=1∞​(3+8n2)(2n2+1)​​ converges or diverges, I'll use the Direct…

Q: p(a) = 0.65, P9b) = 0.56, P(a and b) = 0.4, find p( a or b

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Q: 7

A:

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…

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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) = 0.16, 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: 4 = 70, find n.

A:

Q: given that P(A or B) = 1/3, P(A) = 1/7, and P(A and B) = 1/8, find P(B) a. 101/168 b. 159/168 c.…

A: Concept of General Addition Rule: For any two events A and B the General Addition Rule states that:\

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: Use the following matrices and find an elementary matrix E that satisfies the stated equation. =( A…

A: The given matrices are:

Q: r(z) = 31* +41² + 71 + 4,

A: Express mathematically the definition of derivative. f'(x)=Lth→0f(x+h)-f(x)h Let the given…

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

A: