Advertisements
Advertisements
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?
उत्तर
Probability of success = Probability of getting a total of 9
= Probability of getting (3,6), (4,5), (5,4), (6,3) out of 36 outcomes
\[p = \frac{4}{36} = \frac{1}{9}, q = 1 - p = \frac{8}{9}\text{ and } n = 6\]
\[\text{ X follows a binomial distribution with n} = 6, p = \frac{1}{9} \text{ and } q = \frac{8}{9}\]
\[P(X = r) = ^{6}{}{C}_r \left( \frac{1}{9} \right)^r \left( \frac{8}{9} \right)^{6 - r} \]
\[\text{ The required probability = Probability of at least 5 successes } \]
\[ = P(X \geq 5) \]
\[ = P(X = 5) + P(X = 6)\]
\[ = ^{6}{}{C}_5 \left( \frac{1}{9} \right)^5 \left( \frac{8}{9} \right)^{6 - 5} + ^{6}{}{C}_6 \left( \frac{1}{9} \right)^6 \left( \frac{8}{9} \right)^{6 - 6} \]
\[ = \frac{6(8) + 1}{9^6}\]
\[ = \frac{49}{9^6}\]
APPEARS IN
संबंधित प्रश्न
A coin is tossed 5 times. What is the probability that tail appears an odd number of times?
A fair coin is tossed 8 times, find the probability of exactly 5 heads .
Find the probability of 4 turning up at least once in two tosses of a fair die.
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?
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.
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.
State the sample space and n(S) for the following random experiment.
A coin is tossed twice. If a second throw results in head, a die thrown, otherwise a coin is tossed.
A coin and a die are tossed. State sample space of following event.
C: Getting a tail and perfect square.
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.
Find total number of distinct possible outcomes n(S) of the following random experiment.
6 students are arranged in a row for a photograph.
Consider an experiment of drawing two cards at random from a bag containing 4 cards marked 5, 6, 7, and 8. Find the sample Space if cards are drawn without replacement.
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 bag contains 5 red marbles and 3 black marbles. Three marbles are drawn one by one without replacement. What is the probability that at least one of the three marbles drawn be black, if the first marble is red?
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?
Four cards are successively drawn without replacement from a deck of 52 playing cards. What is the probability that all the four cards are kings?
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?
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?
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.
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.
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?
There are two bags, one of which contains 3 black and 4 white balls while the other contains 4 black and 3 white balls. A die is thrown. If it shows up 1 or 3, a ball is taken from the Ist bag; but it shows up any other number, a ball is chosen from the second bag. Find the probability of choosing a black ball.
There are three urns containing 2 white and 3 black balls, 3 white and 2 black balls, and 4 white and 1 black balls, respectively. There is an equal probability of each urn being chosen. A ball is drawn at random from the chosen urn and it is found to be white. Find the probability that the ball drawn was from the second urn.
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 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 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
Two cards are drawn together from a pack of 52 cards. The probability that one is a spade and one is a heart, 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?
An urn contains 5 red and 2 green balls. A ball is drawn at random from the urn. If the drawn ball is green, then a red ball is added to the urn and if the drawn ball is red, then a green ball is added to the urn; the original ball is not returned to the urn. Now, a second ball is drawn at random from it. The probability that the second ball is red is:
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))`.
There are three machines and 2 of them are faulty. They are tested one by one in a random order till both the faulty machines are identified. What is the probability that only two tests are needed to identify the faulty machines?
