Advertisements
Advertisements
प्रश्न
A lot of 100 watches is known to have 10 defective watches. If 8 watches are selected (one by one with replacement) at random, what is the probability that there will be at least one defective watch?
उत्तर
Probability of defective watch out of 100 watches = `10/100 = 1/10`.
Here, n = 8
p = `1/10`
q = `1 - 1/10 = 9/10`
And r ≥ 1
P(X ≥ 1) = 1 – P(x = 0)
= `1 - ""^8"C"_0 (1/10)^0 (9/10)^(8 - 0)`
= `1 - (9/10)^8`
Hence, the required probability is `1 - (9/10)^8`.
APPEARS IN
संबंधित प्रश्न
A coin is tossed 5 times. What is the probability of getting at least 3 heads?
A fair coin is tossed 8 times, find the probability of at most six heads.
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.
In an automobile factory, certain parts are to be fixed into the chassis in a section before it moves into another section. On a given day, one of the three persons A, B, and C carries out this task. A has a 45% chance, B has a 35% chance and C has a 20% chance of doing the task.
The probability that A, B, and C will take more than the allotted time is `(1)/(6), (1)/(10), and (1)/(20)` respectively. If it is found that the time taken is more than the allotted time, what is the probability that A has done the task?
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.
A coin and a die are tossed. State sample space of following event.
A: Getting a head and an even number.
A coin and a die are tossed. State sample space of following event.
B: Getting a prime number.
Two dice are thrown. Write favourable outcomes for the following event.
R: Sum of the numbers on two dice is a prime number.
Also, check whether Events Q and R are mutually exclusive and exhaustive.
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.
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?
Prove that P(A) = `"P"("A" ∩ "B") + "P"("A" ∩ bar"B")`
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?
A and B throw a pair of dice alternately. A wins the game if he gets a total of 6 and B wins if she gets a total of 7. It A starts the game, find the probability of winning the game by A in third throw of the pair of dice.
An urn contains m white and n black balls. A ball is drawn at random and is put back into the urn along with k additional balls of the same colour as that of the ball drawn. A ball is again drawn at random. Show that the probability of drawing a white ball now does not depend on k.
Three bags contain a number of red and white balls as follows:
Bag 1:3 red balls, Bag 2:2 red balls and 1 white ball
Bag 3:3 white balls.
The probability that bag i will be chosen and a ball is selected from it is `"i"/6`, i = 1, 2, 3. What is the probability that a red ball will be selected?
Refer to Question 74 above. The probability that exactly two of the three balls were red, the first ball being red, is ______.
A die is thrown and a card is selected at random from a deck of 52 playing cards. The probability of getting an even number on the die and a spade card is ______.
A flashlight has 8 batteries out of which 3 are dead. If two batteries are selected without replacement and tested, the probability that both are dead is ______.
Two dice are thrown. If it is known that the sum of numbers on the dice was less than 6, the probability of getting a sum 3, is ______.
In a college, 30% students fail in physics, 25% fail in mathematics and 10% fail in both. One student is chosen at random. The probability that she fails in physics if she has failed in mathematics is ______.
A card is drawn at random from a pack of 52 cards. What is the probability that the card drawn is either ace or a king?
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
In year 2019, the probability of getting 53 Sundays is
The probability of getting qualified in JEE-Mains and JEE-Advanced by a student are `1/5` and `3/5` respectively. The probability that the students gets qualified for one of these tests is
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?
Assertion (A): Two coins are tossed simultaneously. The probability of getting two heads, if it is known that at least one head comes up, is `1/3`.
Reason (R): Let E and F be two events with a random experiment, then `P(E/F) = (P(E ∩ F))/(P(E))`.
