Advertisements
Advertisements
Question
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
Solution
Let E1, E2, E3, E4 and E5 be the events that the surgeries are rated as very complex, complex, routine, simple and very simple respectively.
∴ P(E1) = 0.15
P(E2) = 0.20
P(E3) = 0.31
P(E4) = 0.26
And P(E5) = 0.08
P(neither very complex nor very simple) = P(E'1 ∩ E'5)
= P(E1 ∪ E5)' = 1 – P(E1 ∪ E5)
= 1 – [P(E1) + P(E5)]
= 1 – [0.15 + 0.08]
= 1 – 0.23
= 0.77
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?
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:
C = Getting a multiple of 3
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 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?
If three dice are throw simultaneously, then the probability of getting a score of 5 is
If P(A ∪ B) = P(A ∩ B) for any two events A and B, then
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?
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 on the kth roll of the die?
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 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 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. What is the probability that two black balls are chosen?
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}
Calculate P(A), P(B), and P(A ∩ B)
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 P(A ∪ B) = P(A ∩ B) for any two events A and B, then ______.
The probability of intersection of two events A and B is always less than or equal to those favourable to the event A.
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 ______.
