|20. Suppose a fair coin is tossed three times. Let A be the event that a head appears on the first toss, and let B be the event that an even number of heads is obtained. Show that P(A|B) = P(A) and P(B| A) = P(B).

Q: Find P(A and B) if P(A) is 0.3 and the P(B) is 0.4, and events A and B are independent.

A:

Q: Suppose that in a given town, 60% of the population is under age 40 (event A). It is found that the…

A: GivenEvent A represent population under age 40P(A)=0.60Event B is who support mandatory…

Q: Suppose that ?(?)= 0.7 and ?(?)= 0.2. If both events are disjoint, then what is ?(? ?? ?)?  (a) 0…

A: Solution

Q: 1a) Let E be the event that a corn crop has an infestation of earworms, and let B be the event that…

A: a) Given  Let E be the event that a corn crop has an infestation of earworms, and let B be the event…

Q: A computer-consulting firm presently has bids out on two projects. Let A= [awarded project 1] and B=…

A: Given: PA=0.75, PB=0.35 and PA∩B=0.2.

Q: Example 2.3.11 Show that for any two events A and B, P(AN B) s P(A) s P(A U B) s P(A) + P(B) nned…

A:

Q: b) Let A be the event that a family has children of both sexes and B be the event that a family has…

A: According to given conditions: A= Event representing that a family has children of both sexes. B=…

Q: In a simultaneous throw of a pair of fair 6-sided dice, find the probability of getting: d. A sum…

A: Solution: Note: Hello! As you have posted more than 3 sub parts, we are answering the first 3…

Q: 2. A construction company has 5 dump trucks that they can use for their various projects. Let X…

A: (As per Bartle by guidelines, we can answer only three subparts of a given question. We shall be…

Q: A and B are independent events. If Pr[A]=0.5 and Pr[B]=0.7, what is Pr[A∩B′]?

A:

Q: assume that Pr[A∪B]=0.6 and Pr[A]=0.2 (1) What is Pr[B] if A and B are independent events?

A: Since A and B are independent event, so pr(A∩B)= pr(A)pr(B).

Q: 3 4 Q4) Suppose a class contains girls, and boys. Suppose that 40% of the girls have long hair, and…

A: Above question is solved.

Q: Suppose A and B are two independent events with P(a)=0.5 and P(b)=0.4 what is the P(A U B)?

A:

Q: Suppose that A and B are two events such that P(A) + P(B) < I. a What is the smallest possible value…

A: Given, A and B are two events such that P(A)+P(B)&lt;1

Q: r of matches where the football matches of Galatasaray football team were postponed due to bad…

A: Consider X be the random variable representing the number of matches where the football matches of…

Q: Q1: If the event A is independent with itself, then P(A) is

A: The statement is the event A is independent itself.

Q: Question * For two independent events A and B, if P(A OB) = 0,049 and P(A) = 10P(B), then P(A) is…

A: We have given that,  We have two independent events A and B and P(A∩B) = 0.049 and P(A) = 10P(B)…

Q: 7-The probability that the event P(E) will accur is between a- 0<P(E) <1 b- 0≤P(E) ≤1 C- 0≤P(E) <1…

A:

Q: pany offers a subsidy to any family whose electricity consumption is less than 240kWh during a given…

A: The probability that consumption will not exceed in any of month P(A∩B) = P(A) +P(B) -P(A∪B)…

Q: 1x* If the Event A must occur with certainty, then the probability of this event is in between O…

A: Given: If the Event A must occur with certainty, then the probability of this event is in between 0…

Q: Disks of polycarbonate plastic from a supplier are analyzed for scratch and shock resistance. The…

A: P(A) = (70 + 16) / 100 = 86 / 100 = 0.86 P(B) = (70 + 9) / 100 = 79 / 100 = 0.79 P(AB) = Probability…

Q: (c) State an event which is (i) complementary with G; (ii) mutually exclusive with M.

A: Event: In probability theory, an event is an outcome or a set of outcomes of a random experiment to…

Q: 14. (i) A and B are two events such that P(4) = 1/4, P(B) = 1/3, and P(4 - B) = 1/2, Find PUB/A).…

A:

Q: (1) Suppose an influenza epidemic strikes a city. In 10% of families the mother has influenza; in…

A: Given that, a family with a mother, father, and two children. Let A₁ = {mother has influenza), A₂ =…

Q: Compute the probability of each of the following events: (a) X< 1.5 (b) XY even (c) Y is even given…

A:

Q: 7. Consider randomly selecting a student at a certain university, and let A denote the event that…

A: a. Addition rule: For any two events A and B, P(A∪B)=P(A)+P(B)−P(A∩B) The probability of the…

Q: Compute the probability of each of the following events (i) X <1 1/2 (ii) XY is even

A:

Q: A dice is rolled once. Let E be the event of an even number coming up, O the event of an odd number…

A: From the given information we want to know the event are independent or not.

Q: Q7. The probability that the USA Embassy will locate in a city A of certain country is 0.7, the…

A: we have to find probability that the industry will locate in neither city...

Q: A balanced die is tossed twice. If A is the event thatan even number comes up on the first toss, B…

A: Given Events:   A:  Even number comes up on the first toss B: Even number comes up on the second…

Q: when 3 coins are tossed if Arepresent an event that appears at most re, the complement of the event…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: (b) When a soldier fires at a target, the probability that he hits the 1 target in - for solider A,…

A:

Q: Suppose that A and b are events such that P(A) = 0.75 and P(A&amp;B) = 0.25. Determine P(B|A).

A:

Q: When two events cannot occur at the same time, they are said to be OA mutually exclusive. OB. not…

A: In this case, we need to find the suitable option for the given statement.

Q: 1. These are the events that cannot happen at the same time. a. mutually exclusive b. non mutually…

A:

Q: Suppose that at Indiana State University, 35% of students are international students. What is the…

A: Solution-: Given: n=100,p=0.35 We find, P[40 students out of a randomly sampled group of 100 are…

Q: If the Event A must occur with certainty, then the probability of this event is in * .(between O and…

A:

Q: Suppose that AA and BB are two independent events for which P(A)=0.18 and P(B)=0.8 . Find each of…

A: Two events A and B are said to be independent if; P(A and B)=P(A)×P(B)

Q: Suppose that E and F are two events and that P(E and F)=0.48, P(F)=0.55, and P(E)=0.5. What is P(F…

A: Suppose that E and F are two events and that P(E and F)= 0.48 P(F)=0.55 and P(E)=0.5 What is P(F |E)…

Q: 6. Imagine that a zealous prosecutor (P) has accused a defendant (D) of com- mitting a crime.…

A:

Q: The probability of a medical intervention being successful is 0.65. What is the probability that 8…

A:

Q: 14 - The number of storms that occur in the Mediterranean region between 20-30 March is equal to 3…

A: Let X represent the random variable   X~ Poisson (3)

Q: Consider the following two events for a randomly selected adult: Y = N = this adult has shopped on…

A:

Q: (1) A witch is planting a garden. In one of her garden beds, she plants peppers with probability…

A: Given that, witch is planting a garden. In one of her garden beds, she plants peppers with…

Q: In any given turn while playing a board game, the probability that a player will win a second turn…

A:

Q: Let A be the event that a family has children of both sexes and B be the event that a family has at…

A: Two events A and B are said to be independent if P(A and B) = P(A)P(B).

Q: - The probability of a traffic accident case coming to the emergency department of a hospital in a…

A:

Q: A sample of 20 products are selected from output of a production line which contains 6 defective…

A: Out of 20, 6 are not effective. The event of drawing the products one after the other will be…

Q: A couple has two children. Let A be the event that their first child is a boy and note that P(A) =…

A: