Home
Class 12
MATHS
A box contains 100 bulbs out of which 10...

A box contains 100 bulbs out of which 10 are defective. A sample of 5 bulbs is drawn. The probability that none is defective , is

A

`10^(-1)`

B

`((1)/(2))^(5)`

C

`((1)/(10))^(5)`

D

`(9)/(10)`

Text Solution

Verified by Experts

The correct Answer is:
C
The repeated selection of bulbs from a box are Bernoulli trials . Let X denotes the number of defective bulbs out of a sample of 5 bulbs.
Now, probability of getting a defective bulbs.
`p=(10)/(100)=(1)/(10)`
and `q=1-p=1-(1)/(10)=(9)/(10)`
clearly, X is binominal distribution with n=5
`p=(1)/(10) and q=(9)/(10)`
`therefore P(X=r)=""^(n)C_(r)p^(r)q^(n-r)`
`=""^(5)C_(r).((1)/(10))^(r)((9)/(100))^(5-r)`
P(all bulbs ares defective
`=P(X=5)=""^(5)C_(5)*((1)/(10))^(5)((9)/(10))^(0)`
`=((1)/(10))^(5)`
Promotional Banner

Topper's Solved these Questions

  • BINOMIAL DISTRIBUTION

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise Exercise 1 (Topical problems) (Mean and Variance|7 Videos

  • BINOMIAL DISTRIBUTION

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise Exercise 2 (MISCELLANEOUS PROBLEM) (Mean and Variance|32 Videos

  • APPLICATIONS OF DERIVATIVES

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET CORNER|21 Videos

  • CIRCLE AND CONICS

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise All Questions|74 Videos

Similar Questions

Explore conceptually related problems

A box contains 10 bulbs,of which just three are defective.If a random sample of five bulbs is drawn,find the probabilities that the sample contains: Exactly on defective bulb. Exactly two defective bulbs.No defective bulbs.

A box contains 40 pens out of which x are non-defective. If one pen is drawn at random, the probability of drawing a non defective pen is y. If we replace the pen drawn and then add 20 more non-defective pens in this bag, the probability of drawing a non-defective pen is 4y. Then, evaluate the value of x.

A box contains 40 pens out of which x are non-defective. If one pen is drawn at random, the probability of drawing a non-defective pen is y. If we replace the pen drawn and then add 20 more non-defective pens in this bag the probability of drawing a non-defective pen is 4y. Then, evaluate the value of x.

A box contains 10 sample watches, 2 of which are defective. If 2 are selected at random, the probability that both selected are defective is,

A box contains 100 bulbs 20 of which are defective.10 bulbs are selected for inspection. Find the probability that: i.all 10 are defective ii.all 10 are good ii.at least one is defective iv. none3is defective.

In a box containing 100 bulbs, 10 are defective. What is the probability that out of a sample of 5 bulbs, (i) none is defective and (ii) exactly 2 are defective ?

A box contains 13 bulbs out of which 5 bulbs are defective. 3 bulbs are drawn one by one from the box without replacement. Find the probability that exactly 2 bulbs are defective.

A box contains 16 bulbs out of which 4 bulbs are defective. 3 bulbs are drawn one by one from the box without replacement. Find the probability that all three are defective bulbs