b. In a survey of 200 college students, it was found that; 120 study mathematics, 70 study chemistry, 30 study physics and chemistry, 20 study none of these subjects. Depict the events "A: Mathematics", "B: Physics" and "C: Chemistry" on the given Venn- Diagram, and find the number of the students who studies all the three subjects. 90 study physics 40 study mathematics and physics, 50 study chemistry and mathematics A and 8 not C only A only B A. B and B and Cnot A A and Cnot B

Q: One card is selected from an ordinary 52 card deck with an event A as "seleet a King", B as "select…

A:

Q: A and B are events with P(A)=0.3, P(A OR B)=0.89, and P(A AND B)=0.01, find P(B).

A: Given that ; If A and B are events with P(A)=0.3, P(A OR B)=0.89, P(A AND B)=0.01, find P(B) By…

Q: Given P(A) = 0.37 , P(B) = 0.38 , and P(AorB) = 0.27 , are events A and B mutually exclusive?

A:

Q: Given P(A and B) = 0.16, P(A) = 0.20, and P(B) = 0.80 are events A and B independent or dependent?

A: GivenP(A)=0.20P(B)=0.80P(A∩B)=0.16

Q: In how many different order could the police department arrange six suspects in a police lineup if…

A: In this question we will use basic of permutations and combinations and concept of probability and…

Q: Given P(A) = 0.47, P(B) = 0.41, and P(A or B) = 0.88, are events A and B mutually exclusive?…

A: Events A and B are mutually  exclusive when  Hence, Event A and B are mutually exclusive.

Q: If A and B are events with P(A)=0.2, P(A OR B)=0.74, and P(A AND B)=0.06, find P(B).

A:

Q: If A and B are disjoint events, then which statement below is true? OP(AIB)-0 OP(A and B) = 0 OP(A…

A: Given that, A and B are two disjoint events.

Q: If A and B are events with P(A)=0.6, P(A OR B)=0.98, P(A AND B)=0.02, find P(B).

A:

Q: Given P(A) = 0.31, P(B) = 0.98, P(C) = 0.97 and that events A, B, and C are independent, what is…

A:

Q: Given P(A) = 0.62, P(B) = 0.78, P(C) = 0.61 and that events A, B, and C are independent, what is…

A:

Q: Given P(A) = 0.47, P(B) = 0.41, and P(A or B) = 0.88, are events A and B mutually exclusive?

A: Mutually exclusive events: The two events A and B are mutually exclusive events, then probability P…

Q: Suppose events A and B are NOT disjoint, and that P(A) = 0.3 and P(B) = 0.15. What is P(A or B)? 2.…

A: Disjoint events:   Let A and B be any two events, if the events A and B are mutually exclusive or…

Q: A,B and c are events: P(A)=.35, P(B)=.45, P(C)=.55. Which of these events, if any could be…

A: The probability of event A (say) and the probability of its compliment is equal to 1.

Q: Given P(A) = 0.35, P(B) = 0.08, and P(A or B) = 0.43, are events A and B mutually exclusive?

A: Given: P(A) = 0.35 P(B) = 0.08 and P(A or B) = 0.43

Q: Given P(A) = 0.51, P(B) = 0.79, and P(A or B) = 0.66, are events A and B mutually exclusive?

A:

Q: 6 Given P(A)=and P(B)= a. If P(AUB) = determine whether A and B are mutually exclusive or…

A: It is given that, P(A)=3/4 P(B)=2/3

Q: If A and B are independent events with P(A) = 0.5 and P(A ∩ B) = 0.12, then, P(B) = Question 27…

A:

Q: Consider 3 events as illustrated in the following Venn diagram. A1 A2 0.02 0.05 0.03 0.20 0.06 0.09…

A: Solution

Q: 1. Suppose you have five quizzes in a course, and you classify the level of difficulty of each…

A: Given Information: Number of quizzes in a course = 5  Levels of difficulty = 3 (low , medium , high)

Q: 2. If A, B and C'are mutually exclusive and exhaustive events, 17-14 find P (B) if P(C) =P(A) = P…

A:

Q: given p(a)=0.23, P(B)=0.05, P(C)=0.65 and that events A,B and C are independent, What is P(A,B, and…

A: given p(a)=0.23, P(B)=0.05, P(C)=0.65 and that events A,B and C are independent, What is P(A,B, and…

Q: a)Suppose events E and F are mutually exclusive with P(E)= 0.15 and P(F)= 0.75. (i) What is the…

A: We have given that  P(E)= 0.15 and P(F)= 0.75. IF A and B are mutually exclusive.  P ( A U B ) = 0…

Q: In parts (a) and (b), identify whether the events are Mutually Exclusive, Independent, or Neithe…

A: (a) If the probability of occurrence of one event is not affected by the probability of occurrence…

Q: Given P(A) = 0.92, P(B) = 0.33, and P(A or B) = 0.40, are events A and B mutually exclusive?

A: Given Data: P(A) = 0.92 P(B) = 0.33 P(A or B) = 0.40

Q: Given P(A)=0.31, P(B)=0.49 and P(A or B)=0.78, are events A and B mutually exclusive

A: According to the given information, we have P(A) = 0.31 P(B) = 0.49 P(A or B) = 0.78

Q: Suppose two events, A and B, are defined where P(A)=P(B)=.4 and P(AorB)=.65. What is P(AandB)

A: Given : P(A)=P(B)=.4 and P(AorB)=.65

Q: Let A and B be events with P(4) =0.3, P(B) =0.73, and P(B 4) = 0.9. Find P(A and B). P(4 and B) =

A: Given data:

Q: Consider 3 events as illustrated in the following Venn diagram. S A1 A2 0.02 0.05 0.03 0.20 0.06…

A:

Q: Given P(A) = 0.82, P(B) = 0.52, P(C) = 0.79 and that events A, B, and C are independent, what is…

A: Obtain the probability that the three events A, B and C are independent events. The probability that…

Q: Nicole packs 3 blouses (A, B, C) and 2 skirts (D, E). c. If event M is wearing blouse C or skirt E,…

A: Given: There are 3 blouses(A,B,C) and 2 skirts(D,E)

Q: Construct a Venn Diagram showing three overlapping events A, B and C. Shade the region corresponding…

A:

Q: If A and B are events with P(A)=0.7, P(A OR B)=0.89, and P(A AND B)=0.01, find P(B).

A: Solution-: Given: P(A)=0.7,P(A OR B)=0.89, P(A AND B)=0.01  We find P(B)=?

Q: Given P(A) = 0.78, P(B) = 0.49, P(C) = 0.45 and that events A, B, and C are independent, what is…

A: Given, P(A) = 0.78 P(B) = 0.49 P(C) = 0.45  that events A, B, and C are independent.       To find,…

Q: Given P(A) = 0.27, P(B) = 0.19, and P(A or B) = 0.46, are events A and B mutually exclusive

A: Given,  P(A) = 0.27 P(B) = 0.19 P(A or B) = 0.46

Q: If A and B are independant events with P(A) = 0.295, P(B) = 0.32, then P(A | B) =

A: It is given that A and B are independent. P(A) = 0.295, P(B) = 0.32

Q: Given P(A) = 0.21, P(B) = 0.99, P(C) = 0.31 and that events A, B, and C are independent, what is…

A: We have given that  P(A) = 0.21, P(B) = 0.99, P(C) = 0.31 And events A, B and C are independent.

Q: Given P(A) = 0.20, P(B) = 0.30, and P(A or B) = 0.50, are events A and B mutually exclusive?

A: Solution: Mutually exclusive events: Two events A and B are said to be mutually exclusive when the…

Q: If A and B are events with P(A)=0.3, P(A OR B)=0.91, and P(A AND B)=0.09, find P(B).

A: Given that, A and B are two events, P(A) = 0.3 P(A or B) = 0.91 P(A and B) = 0.09

Q: Given the following information about events B and C: P(B)=70% P(B AND C)=0 P(C)=45% Are B and C

A: If the two events are mutually exclusive then their intersection part is zero.  That is , the two…

Q: 11. Given P(A) = 0.52, P(B) = 0.87, P(C) = 0.06 and that events A, B, and C are independent, what is…

A: It is mentioned that the events A, B and C are independent. The probabilities are provided as; P(A)…

Q: Given P(A) = 0.21, P(B) = 0.11, and P(A or B) = 0.23, are events A and B mutually exclusive?

A:

Q: Given P(A)=0.37, P(B)=0.38, and P(A or B)=0.27, are events A and B mutually exclusive?

A: If A and B are mutually exclusive then P(A or B) = P(A) + P(B) Here, P(A or B) = 0.27 and P(A) +…

Q: For a group of 300 cars the numbers, classified by colour and country of manufacture, are shown in…

A: Solution: The given table of data is

Q: 13. It is given that 1 P (A, + A2) = 6' P (A,42) = P (Ã) = Show that the events Aj and A2 are…

A:

Q: Suppose three events namely A1, A2, and A3. Show that P(A, U A, U A, ) = P(A,)+ P(A,)+ P(A,) iff…

A:

Q: Given P(A) = 0.34, P(B) = 0.60, and P(A or B) = 0.24, are events A and B mutually exclusive?

A: We have given that- P(A) = 0.34 P(B) = 0.60 P(A or B) = 0.24 We know that two events are mutually…

Q: Thirty-five percent of the cars in Israel are new. Out of the new cars, 60% are white. Overall, 45%…

A:

Q: Given P(A) = 0.34, P(B) = 0.60, P(C) = 0.21 and that events A, B, and C are independent, what is…

A:

Q: Consider three events A, B, and C. Given- P(A) = 0.3, P(B) = 0.6, P(C) = 0.2, P(A ∩ C) = 0, P(B|C) =…

A: It is given that P(A∩C)=0 and asked to find the value of P(A∩B∩C). P(A∩C)=0 means there is no common…

Addition Rule of Probability

It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.

Expected Value

When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).

Probability Distributions

Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.

Basic Probability

The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.