Show that the multiplication law P(A B) = P(A/B) P(B), established for two events, be generalized to three events as foilows; may P(AOBOC) = P(A/BOC) P(B/C) P(C)

Q: Suppose that 2 cards are drawn from a well-shuffled deck of 52 cards. What is the probability that…

A: select 2 cards from 52 card deck  there are j,q,k of each 4 suits are face cards  so no. of face…

Q: When Ann drives to school, she only passes one intersection with a stoplight. Based on her previous…

A: given data  P(green or yellow) = 0.70 P(red) = 1 - 0.70 = 0.30 drives to school for 5 days.…

Q: Prove that if P( A ) = 7/50 , P ( B ) = 1/4 and P(A U B) =3/10, then A and B are inclusive events

A:

Q: For any two events A and B and P(B) ÷ 1 and A N B = Ø, find weather the following statement is true…

A: If there are n mutually exclusive, exhaustive and equally likely outcomes of a random experiment and…

Q: Given that P(A) = 0.7, P (A/B) = 0.7, P(A∩B) notation same as P (A and B) = 0.42, find  the…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: 3. A and B are events such that P(A) = 0.2 and P(A U B) = 0.5. Find P(B) in each of the following…

A: There are two events A and B are given.The given probabilities are as follows

Q: 1) Events A and B are mutually exclusive. P(A) = 0.35, P(B) = 0.56. Find a) p(not A) b) p(A and B)…

A: As per Bartley guideline expert have to answer first question only since I had done all for you.

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 A and B be two events such that P(A)3D0.9, P(B)-D0.5, and P (A U B) =0.6. Find: a) P(AnB) b)…

A: Disclaimer: Since you have posted a question with multiple subparts, we will solve first 3 subparts…

Q: A lot of 10 components contains 4 that are defective. Two components are drawn at random and tested.…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: and red) totaling 25 balls. If ive blue balls are added to he probability of drawing a vill be…

A: *Answer:

Q: 5. The probability that at least one of the events A and B will occur is P(A ∪ B) = P(A) + P(B) −…

A: and

Q: If A, B, and C are any three events then O a PAUBUC)= P(A) + (B) + P(C)-PANBNC) O b.…

A:

Q: The box contains b white, c black and p blue balls. Balls are randomly drawn from the box without…

A: b=white ballC=black ball p =blue ball

Q: If two events, A and B,

A: Since you have posted a question with multiple subparts, we will solve the first three subparts for…

Q: let a and b be two events with P(A) = 3/8, P(B) = 3/8, and P(A∩B) = 1/8. the value of P(A U B) is

A: From the provided information, P (A) = 3/8 P (B) = 3/8 P (A ∩ B) = 1/8

Q: For any two events A and B it is known that P(A) = 2/3, P(AUB) = 7/12 and P(A∩B) = 5/12, find P(B

A:

Q: Suppose that P(A)=1/4 and P(B)=1/3. Assuming that A and B are mutually exclusive events, calculate:…

A: P(A) = 14P(B) = 13independent events.

Q: The table displays the number and type of tickets bought for a baseball tournament held on a…

A:

Q: Suppose P(A) = .2, P(B) = .5, and P(A and B) = .1. What is P(A or B)?

A:

Q: Let the events A and B be Such that PrAC) = to +10)%, PIB)= (8+15)%. Find P (AUB), if 1= A and B are…

A: If A and B denote two events, the probability PA∪B denotes the probability of either of the events…

Q: Let A and B be events such that P(A)=1/4, P(A or B)=1/3, and P(A and B)=1/5. DetermineP(B)

A:

Q: 42 a. (a) For any two events A and B, show that P (A) + P(B)-1 P(B) P (B), show that P (B/A) (c) If…

A:

Q: For two events, A and B, we have P(A) = 0.8, P(B) = 0.7, and P(AUB) = 0.9. Then, the value for P(BA)…

A: Given that  P(A) = 0.8, P(B) = 0.7, and P(A U B) = 0.9.

Q: Suppose that A and B are events such that P (A|B) = P (B|A) , P(AUB) = 1, and P(An B) > 0. Prove…

A: Solution: From the given information,

Q: For any three events A, B and C P ( A U BUC) = P(A) + P (B ) + P ( C ) – P ( A OB)-P( BnC) -P(CnA)+…

A:

Q: For two events ,A and B,P(A)=0.4, P(B)=0.2 and ,p(A|B)=0.6 Find a)p(A ∩B) b)p(B|A) c)p(B,|A)

A:

Q: Two events, A and B, are such that P(A∪B) = 0.86, P(B) = 0.72 and P(A) = 0.64. Determine P(AUB)'

A: Given data, P(A∪B) = 0.86 P(B) = 0.72  P(A) = 0.64 P(AUB)' =?

Q: A f cards Contains 13 clubs, stanclard deck of dliamonds, 13 hearts and 13 Spades. I Five carcds are…

A: From the given information, Total number of cards = 52 Thus, the required probability can be…

Q: If 4 married couples and 2 unmarried persons are arranged in a row, find the probability that no…

A: Let Ei = the ith couple sitting together where i = 1,2, 3,4 Then : P(E1) = 2×9!10! = 210=15 P(E1∩E2)…

Q: Let A and B be independent events with P(A) = 0.2 and P(B) = 0.3. Find: BAO REALT DORI

A: Hello! As you have posted more than 3 sub-parts, we are answering the first 3 sub-parts.  In case…

Q: (b) There are four basic human blood groups: A, B, AB and O. Of UK blood donors, about 37% are type…

A: Given information: There are four basic blood groups, A, B, AB and O.…

Q: Q2) Two cards are drawn simultaneously from a well shuffled pack of cards. Find the probability of…

A:

Q: a) Show that for any three events A, B, and C, the probability that at least one of them occurs is…

A: Given  We need to prove that for three events A,B and C,the probability that atleast one of them…

Q: Suppose that we have two events, A and B, with P(A)=0.60,P(B)=0.70, and P(A∩B)=0.40 a. Find P(A∣B)…

A:

Q: For any two events A and B; P (AUB) = P (A) + P (B) – P ( A nB) %3D

A:

Q: Which of the following is NOT necessarily true for mutually exclusive events A and a) P(A NB)=0 c)…

A: Mutually Exclusive events: If A and B mutually exclusive events, then PA∩B=0. a) From the mutually…

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: a) Two events, A and B, are such that P(AUB) = 0.86, P(B) = 0.72 and P(A) = 0.64. Determine (i) P…

A: Given: A and B are two events PA=0.64PB=0.72PA∪B=0.86

Q: The general multiplication rule says that P(A and B)=_______If A and B are events, the…

A: Here given , The general multiplication ,  multiplication rule  P(A and B) = P(A). P(B).

Compound Probability

Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent. 

Tree diagram

Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axioms express probability in terms of a probability space, which assigns a measure with values ranging from 0 to 1 to a set of outcomes known as the sample space. An event is a subset of these outcomes that is described. 

Conditional Probability

By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between 0 and 1. The higher the chance of an event occurring, the closer is its value to be 1. If the probability of an event is 1, it means that the event will happen under all considered circumstances. Similarly, if the probability is exactly 0, then no matter the situation, the event will never occur.