Advertisements
Advertisements
प्रश्न
By examining the chest X ray, the probability that TB is detected when a person is actually suffering is 0.99. The probability of an healthy person diagnosed to have TB is 0.001. In a certain city, 1 in 1000 people suffers from TB. A person is selected at random and is diagnosed to have TB. What is the probability that he actually has TB?
उत्तर
Let E1: Event that a person has TB
E2: Event that a person does not have TB
And H: Event that the person is diagnosed to have TB.
∴ P(E1) = `1/1000` = 0.001
P(E2) = `1 - 1/1000 = 999/1000` = 0.999
`"P"("H"/"E"_1)` = 0.99
`"P"("H"/"E"_2)` = 0.001
∴ `"P"("E"_1/"H") = ("P"("E"_1)*"P"("H"/"E"_1))/("P"("E"_1)*"P"("H"/"E"_1) + "P"("E"_2)*"P"("H"/"E"_2))`
= `(0.001 xx 0.99)/(0.001 xx 0.99 + 0.999 xx 0.001)`
= `0.99/(00.99 + 0.999)`
= `0.990/(0.990 + 0.999)`
= `990/1989`
= `110/221`
Hence, the required probability is `110/221`.
APPEARS IN
संबंधित प्रश्न
A pair of dice is thrown 6 times. If getting a total of 9 is considered a success, what is the probability of at least 5 successes?
A fair coin is tossed 8 times, find the probability of at least six heads
A coin is tossed 5 times. What is the probability that head appears an even number of times?
A problem is given to three students whose chances of solving it are `1/4, 1/5` and `1/3` respectively. Find the probability that the problem is solved.
A pair of dice is thrown. What is the probability of getting an even number on the first die or a total of 8?
Bag A contains 1 white, 2 blue and 3 red balls. Bag B contains 3 white, 3 blue and 2 red balls. Bag C contains 2 white, 3 blue and 4 red balls. One bag is selected at random and then two balls are drawn from the selected bag. Find the probability that the balls draw n are white and red.
An urn contains 25 balls of which 10 balls are red and the remaining green. A ball is drawn at random from the urn, the colour is noted and the ball is replaced. If 6 balls are drawn in this way, find the probability that:
(i) All the balls are red.
(ii) Not more than 2 balls are green.
(iii) The number of red balls and green balls is equal.
In a bolt factory, three machines A, B, and C manufacture 25%, 35% and 40% of the total production respectively. Of their respective outputs, 5%, 4% and 2% are defective. A bolt is drawn at random from the total production and it is found to be defective. Find the probability that it was manufactured by machine C.
State the sample space and n(S) for the following random experiment.
A coin is tossed twice. If a second throw results in a tail, a die is thrown.
Find total number of distinct possible outcomes n(S) of the following random experiment.
From a box containing 25 lottery tickets any 3 tickets are drawn at random.
Find total number of distinct possible outcomes n(S) of the following random experiment.
5 balls are randomly placed into 5 cells, such that each cell will be occupied.
A card is drawn at random from an ordinary pack of 52 playing cards. State the number of elements in the sample space if consideration of suits is taken into account.
Box-I contains 8 red (R11, R12, R13) and 2 blue (B11, B12) marbles while Box-II contains 2 red(R21, R22) and 4 blue (B21, B22, B23, B24) marbles. A fair coin is tossed. If the coin turns up heads, a marble is chosen from Box-I; if it turns up tails, a marble is chosen from Box-II. Describe the sample space.
From a group of 2 men (M1, M2) and three women (W1, W2, W3), two persons are selected. Describe the sample space of the experiment. If E is the event in which one man and one woman are selected, then which are the cases favourable to E?
A car manufacturing factory has two plants, X and Y. Plant X manufactures 70% of cars and plant Y manufactures 30%. 80% of the cars at plant X and 90% of the cars at plant Y are rated of standard quality. A car is chosen at random and is found to be of standard quality. What is the probability that it has come from plant X?
A box has 5 blue and 4 red balls. One ball is drawn at random and not replaced. Its colour is also not noted. Then another ball is drawn at random. What is the probability of second ball being blue?
Ten coins are tossed. What is the probability of getting at least 8 heads?
The probability of a man hitting a target is 0.25. He shoots 7 times. What is the probability of his hitting at least twice?
Two natural numbers r, s are drawn one at a time, without replacement from the set S = {1, 2, 3, ...., n}. Find P[r ≤ p|s ≤ p], where p ∈ S.
Assume that in a family, each child is equally likely to be a boy or a girl. A family with three children is chosen at random. The probability that the eldest child is a girl given that the family has at least one girl is ______.
A box has 100 pens of which 10 are defective. What is the probability that out of a sample of 5 pens drawn one by one with replacement at most one is defective?
The letters of the word "ATTRACTION' are written randomly. The probability that no two T's appear together is
Three horses A, B, Care in a race. A is twice as likely to win as B, and B is twice as likely to win as C. The probability that C wins, P(C) is
A box contains 10 balls, of which 3 are red, 2 are yellow, and 5 are blue. Five balls are randomly selected with replacement. Calculate the probability that fewer than 2 of the selected balls are red?
A bag contains 10 white and 3 black balls. Balls are drawn without replacement till all the black balls are drawn. What is the probability that this procedure will come to an end on the seventh draw?
Bag P contains 6 red and 4 blue balls and bag Q contains 5 red and 6 blue balls. A ball is transferred from bag P to bag Q and then a ball is drawn from bag Q. What is the probability that the ball drawn is blue?
