Advertisements
Advertisements
Question
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?
Solution
Here n = 7
p = 0.25 = `25/100 = 1/4`
And q = `1 - 1/4 = 3/4`
P(X ≥ 2) = 1 – [P(X = 0) + P(X = 1)]
= `1 - [""^7"C"_0 (1/4)^0 (3/4)^7 + ""^7"C"_1 (1/4)^1 (3/4)^6]`
= `1 - [(3/4)^7 + 7/4(3/4)^6]`
= `1 - (3/4)^6 (3/4 + 7/4)`
= `1 - (3/4)^6 (10/4)`
= `1 - 729/4096 xx 10/4`
= `1 - 7290/16384`
= `(16384 - 7290)/16384`
= `9094/16384`
= `4547/8192`
Hence, the required probability is `4547/8192`.
APPEARS IN
RELATED QUESTIONS
There are 6% defective items in a large bulk of items. Find the probability that a sample of 8 items will include not more than one defective item.
A coin is tossed 5 times. What is the probability of getting at least 3 heads?
A coin is tossed 5 times. What is the probability that tail appears an odd number of times?
Find the probability of 4 turning up at least once in two tosses of a fair die.
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?
In a bag, there are three balls; one black, one red, and one green. Two balls are drawn one after another with replacement. State sample space and n(S).
A coin and a die are tossed. State sample space of following event.
B: Getting a prime number.
Find total number of distinct possible outcomes n(S) of the following random experiment.
From a group of 4 boys and 3 girls, any two students are selected at random.
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 with 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?
Prove that P(A) = `"P"("A" ∩ "B") + "P"("A" ∩ bar"B")`
A bag contains 4 white and 5 black balls. Another bag contains 9 white and 7 black balls. A ball is transferred from the first bag to the second and then a ball is drawn at random from the second bag. Find the probability that the ball drawn is white.
Bag I contains 3 black and 2 white balls, Bag II contains 2 black and 4 white balls. A bag and a ball is selected at random. Determine the probability of selecting a black ball.
A die is thrown 5 times. Find the probability that an odd number will come up exactly three times.
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 white ball is selected?
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?
A bag contains (2n + 1) coins. It is known that n of these coins have a head on both sides where as the rest of the coins are fair. A coin is picked up at random from the bag and is tossed. If the probability that the toss results in a head is `31/42`, determine the value of n.
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 box contains 3 orange balls, 3 green balls and 2 blue balls. Three balls are drawn at random from the box without replacement. The probability of drawing 2 green balls and one blue ball is ______.
Eight coins are tossed together. The probability of getting exactly 3 heads 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 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?
Two cards are drawn at random from a pack of 52 cards one-by-one without replacement. What is the probability of getting first card red and second card Jack?
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
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
