Advertisements
Advertisements
Question
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?
Options
`(9/10)^5`
`1/2(9/10)^4`
`1/2(9/10)^5`
`(9/10)^5 + 1/2(9/10)^4`
Solution
`(9/10)^5 + 1/2(9/10)^4`
Explanation:
Here, n = 5
p = `10/100 = 1/10` and q = `1 - 1/10 = 9/10` and r ≤ 1
We know that
P(X = r) = `""^"n""C"_"r" "p"^"r" "q"^("n" - "r")`
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?
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 exactly 5 heads .
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?
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.
A committee of 4 persons has to be chosen from 8 boys and 6 girls, consisting of at least one girl. Find the probability that the committee consists of more girls than boys.
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?
Two dice are thrown. Write favourable Outcomes for the following event.
P: Sum of the numbers on two dice is divisible by 3 or 4.
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 not taken into account.
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.
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?
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?
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 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 ______.
A and B are two students. Their chances of solving a problem correctly are `1/3` and `1/4`, respectively. If the probability of their making a common error is, `1/20` and they obtain the same answer, then the probability of their answer to be correct 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
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))`.
