Question

In: Statistics and Probability

If A and B are independent events, P(A)=0.10, and P(B)=0.66, what is P(B|A)?

If A and B are independent events, P(A)=0.10, and P(B)=0.66, what is P(B|A)?

Solutions

Expert Solution

Here in This Question the detailed answers with step by step is given below,

Definition

The conditional probability of A given B, denoted P(A|B), is the probability that event A has occurred in a trial of a random experiment for which it is known that event B has definitely occurred. It may be computed by means of the following formula:

Rule for Conditional Probability

P(A|B)=P(A∩B)/P(B)

If P(A∩B)=P(A)⋅P(B)P(A∩B)=P(A)·P(B), then A and B are independent.

In a situation in which each of P(A)P(A) and P(B)P(B) can be computed and it is known that A and B are independent, then we can compute P(A∩B)P(A∩B) by multiplying togetherP(A)P(A) and P(B)P(B): P(A∩B)=P(A)⋅P(B).

this is the simple answer of your Question.

Hope you understood then RATE POSITIVE ?. In case of any queries please feel free to ask in comment box.

Thank you.


Related Solutions

(a) If A and B are independent events with P(A) = 0.6 and P(B) = 0.7,...
(a) If A and B are independent events with P(A) = 0.6 and P(B) = 0.7, find P (A or B). (b) A randomly selected student takes Biology or Math with probability 0.8, takes Biology and Math with probability 0.3, and takes Biology with probability 0.5. Find the probability of taking Math. A box contains 4 blue, 6 red and 8 green chips. In how many different ways can you select 2 blue, 3 red and 5 green chips? (Give...
A) If two events A and B are​ __________, then​ P(A and ​B)=​P(A)​P(B). complements independent simple...
A) If two events A and B are​ __________, then​ P(A and ​B)=​P(A)​P(B). complements independent simple events mutually exclusive B) The sum of the probabilities of a discrete probability distribution must be​ _______. less than or equal to zero equal to one between zero and one greater than one C) Which of the below is not a requirement for binomial​ experiment? The probability of success is fixed for each trial of the experiment. The trials are mutually exclusive. For each...
if A and B are independent events where P(A) = 0.7 and P(B)= .8: 1. P(A...
if A and B are independent events where P(A) = 0.7 and P(B)= .8: 1. P(A ^ B) = 2. P(~A^~B) = 3.P(A U B) = 4. Does your anwser change if they were dependent?
Q. Let A, B independent events, with P(A) = 1/2 and P(B) = 2/3. Now C...
Q. Let A, B independent events, with P(A) = 1/2 and P(B) = 2/3. Now C be an event with P(C) = 1/4, and suppose that P(A|C) = 1/3, P(B|?̅) =7/9, P(A∩B|?̅) = 7/18. (a) Calculate the P(A∩B) (b) Calculate the P(A|?̅) and P(B|C) (c) Calculate the P(A∩B|C) (d) Show if P(A∩B|C) equals P(A|C)P(B|C) or not.
If A, B, and C events are independent, check if B and A \ C events...
If A, B, and C events are independent, check if B and A \ C events are independent or not.
Let A, B and C be mutually independent events of a probability space (Ω, F, P),...
Let A, B and C be mutually independent events of a probability space (Ω, F, P), such that P(A) = P(B) = P(C) = 1 4 . Compute P((Ac ∩ Bc ) ∪ C). b) [4 points] Suppose that in a bicycle race, there are 19 professional cyclists, that are divided in a random manner into two groups. One group contains 10 people and the other group has 9 people. What is the probability that two particular people, let’s say...
Probability Let A, B and C be Boolean variables denoting three independent events with P(A=1) =...
Probability Let A, B and C be Boolean variables denoting three independent events with P(A=1) = 0.7, P(B=1) = 0.3, and P(C=1) = 0.1. Let D be the event that at least one of A and B occurs, i.e., D = A OR B. Let E be the event that at least one of B and C occurs, i.e., E = B OR C. Let F be the event that exactly one of A and B occurs, i.e., F =...
We are told that events A and B are independent. In addition, events A and C...
We are told that events A and B are independent. In addition, events A and C are independent. Is it true that A is independent of B ∪ C? Provide a proof or counterexample to support your answer.
On the overlap of two events, suppose two events A and B , P(A)=1/2, P(B)=2/3, but...
On the overlap of two events, suppose two events A and B , P(A)=1/2, P(B)=2/3, but we have no more information about the event, what are the maximum and minimum possible values of P(A/B)
True or False? For any two events A and B, P(A∩ B) ≥ 1 − P(A∪...
True or False? For any two events A and B, P(A∩ B) ≥ 1 − P(A∪ B) True or False? For any two independent events A and B, P(A| B) = P(A| Bc ) Compute B(6, .2, 2)
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT