Advertisements
Advertisements
Question
A and B are two events such that P (A) = 0.54, P (B) = 0.69 and P (A ∩ B) = 0.35. Find
\[P (\bar{ A } \cap \bar{ B } )\]
Solution
Given:
P (A) = 0.54, P (B) = 0.69 and P (A ∩ B) = 0.35
\[P\left( \bar{A} \cap \bar{ B } \right) = 1 - P\left( A \cup B \right)\]
= 1 - 0.88
= 0.12
APPEARS IN
RELATED QUESTIONS
A die is thrown. Describe the following events:
- A: a number less than 7
- B: a number greater than 7
- C: a multiple of 3
- D: a number less than 4
- E: an even number greater than 4
- F: a number not less than 3
Also find A ∪ B, A ∩ B, B ∪ C, E ∩ F, D ∩ E, A – C, D – E, E ∩ F', F'
Three coins are tossed once. Let A denote the event "three heads show", B denote the event "two heads and one tail show". C denote the event "three tails show" and D denote the event "a head shows on the first coin". Which events are
- mutually exclusive?
- simple?
- compound?
Two dice are thrown. The events A, B and C are as follows:
A: getting an even number on the first die.
B: getting an odd number on the first die.
C: getting the sum of the numbers on the dice ≤ 5
Describe the events
- A'
- not B
- A or B
- A and B
- A but not C
- B or C
- B and C
- A ∩ B' ∩ C'
In a single throw of a die describe the event:
A = Getting a number less than 7
In a single throw of a die describe the event:
B = Getting a number greater than 7
In a single throw of a die describe the event:
D = Getting a number less than 4
In a single throw of a die describe the event:
F = Getting a number not less than 3.
Also, find A ∪ B, A ∩ B, B ∩ C, E ∩ F, D ∩ F and \[ \bar { F } \] .
A and B are two events such that P (A) = 0.54, P (B) = 0.69 and P (A ∩ B) = 0.35. Find
P (A ∪ B).
A and B are two events such that P (A) = 0.54, P (B) = 0.69 and P (A ∩ B) = 0.35. Find
P (B ∩ \[\bar{ A } \] )
A dice is thrown twice. What is the probability that at least one of the two throws come up with the number 3?
One number is chosen from numbers 1 to 100. Find the probability that it is divisible by 4 or 6?
Probability that a truck stopped at a roadblock will have faulty brakes or badly worn tires are 0.23 and 0.24, respectively. Also, the probability is 0.38 that a truck stopped at the roadblock will have faulty brakes and/or badly working tires. What is the probability that a truck stopped at this roadblock will have faulty breaks as well as badly worn tires?
If a person visits his dentist, suppose the probability that he will have his teeth cleaned is 0.48, the probability that he will have a cavity filled is 0.25, the probability that he will have a tooth extracted is 0.20, the probability that he will have a teeth cleaned and a cavity filled is 0.09, the probability that he will have his teeth cleaned and a tooth extracted is 0.12, the probability that he will have a cavity filled and a tooth extracted is 0.07, and the probability that he will have his teeth cleaned, a cavity filled, and a tooth extracted is 0.03. What is the probability that a person visiting his dentist will have atleast one of these things done to him?
An experiment consists of rolling a die until a 2 appears. How many elements of the sample space correspond to the event that the 2 appears not later than the k th roll of the die?
In a large metropolitan area, the probabilities are 0.87, 0.36, 0.30 that a family (randomly chosen for a sample survey) owns a colour television set, a black and white television set, or both kinds of sets. What is the probability that a family owns either anyone or both kinds of sets?
A team of medical students doing their internship have to assist during surgeries at a city hospital. The probabilities of surgeries rated as very complex, complex, routine, simple or very simple are respectively, 0.15, 0.20, 0.31, 0.26, .08. Find the probabilities that a particular surgery will be rated complex or very complex
A team of medical students doing their internship have to assist during surgeries at a city hospital. The probabilities of surgeries rated as very complex, complex, routine, simple or very simple are respectively, 0.15, 0.20, 0.31, 0.26, .08. Find the probabilities that a particular surgery will be rated neither very complex nor very simple
A team of medical students doing their internship have to assist during surgeries at a city hospital. The probabilities of surgeries rated as very complex, complex, routine, simple or very simple are respectively, 0.15, 0.20, 0.31, 0.26, .08. Find the probabilities that a particular surgery will be rated routine or complex
One urn contains two black balls (labelled B1 and B2) and one white ball. A second urn contains one black ball and two white balls (labelled W1 and W2). Suppose the following experiment is performed. One of the two urns is choosen at random. Next a ball is randomly chosen from the urn. Then a second ball is choosen at random from the same urn without replacing the first ball. What is the probability that two balls of opposite colour are choosen?
A sample space consists of 9 elementary outcomes e1, e2, ..., e9 whose probabilities are
P(e1) = P(e2) = 0.08, P(e3) = P(e4) = P(e5) = 0.1
P(e6) = P(e7) = 0.2, P(e8) = P(e9) = 0.07
Suppose A = {e1, e5, e8}, B = {e2, e5, e8, e9}
List the composition of the event A ∪ B, and calculate P(A ∪ B) by adding the probabilities of the elementary outcomes.
Determine the probability p, for the following events.
An odd number appears in a single toss of a fair die.
Determine the probability p, for the following events.
A king, 9 of hearts, or 3 of spades appears in drawing a single card from a well-shuffled ordinary deck of 52 cards.
Determine the probability p, for the following events.
The sum of 6 appears in a single toss of a pair of fair dice.
The probability that at least one of the events A and B occurs is 0.6. If A and B occur simultaneously with probability 0.2, then `P(barA) + P(barB)` is ______.
If M and N are any two events, the probability that at least one of them occurs is ______.
The probability of intersection of two events A and B is always less than or equal to those favourable to the event A.
If e1, e2, e3, e4 are the four elementary outcomes in a sample space and P(e1) = 0.1, P(e2) = 0.5, P(e3) = 0.1, then the probability of e4 is ______.
