Advertisements
Advertisements
प्रश्न
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?
उत्तर
Let E1 be the event that a family owns colour television set E2 be the event that the family owns black and white television set.
Given that P(E1) = 0.87, P(E2) = 0.36
And P(E1 ∩ E2) = 0.30
∴ The probability that a family owns either colour television set or black and white television set
∴ P(E1 ∪ E2) = P(E1) + P(E2) – P(E1 ∩ E2)
= 0.87 + 0.36 – 0.30
= 0.93
Hence, the required probability = 0.93
APPEARS IN
संबंधित प्रश्न
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'
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:
C = Getting a multiple of 3
In a single throw of a die describe the event:
D = Getting a number less than 4
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
\[P (\bar{ A } \cap \bar{ B } )\]
A and B are two events such that P (A) = 0.54, P (B) = 0.69 and P (A ∩ B) = 0.35. Find
P (A ∩ \[\bar{ B } \] )
A natural number is chosen at random from amongst first 500. What is the probability that the number so chosen is divisible by 3 or 5?
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?
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 simple
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 chosen at random. Next a ball is randomly chosen from the urn. Then a second ball is chosen at random from the same urn without replacing the first ball. Write the sample space showing all possible outcomes
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 card is drawn from a deck of 52 cards. Find the probability of getting a king or a heart or a red card.
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}
Using the addition law of probability, calculate P(A ∪ B)
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.
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}
Calculate `P(barB)` from P (B), also calculate `P(barB)` directly from the elementary outcomes of `barB`
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.
At least one head appears in two tosses of a fair coin.
Determine the probability p, for the following events.
The sum of 6 appears in a single toss of a pair of fair dice.
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 ______.
If A and B are two events associated with a random experiment such that P(A) = 0.3, P(B) = 0.2 and P(A ∩ B) = 0.1, then the value of `P(A ∩ barB)` is ______.
