Home
Class 12
MATHS
Suppose that 90% of people are right-han...

Suppose that 90% of people are right-handed. What is the probability that at most 6 of a random sample of 10 people are right-handed?

Text Solution

Verified by Experts

A person can be either right-handed or left-hended. It is given that `90%` of the people are right-handed. Therefore,
`p=P("right-handed")=9/10`
`q=P("left-handed")=1-9/10=1/10`
Using binomial distribution, the probability that at most six people are right-handed is given by
`underset(r=0)overset(6)sum""^(10)C_(r)p^(r)q^(n-r)underset(r=0)overset(6)sum""^(10)C_(r)((9)/(10))^(r)((1)/(10))^(10-r)`
Therfore, the probability that at most 6 people are right-handed
`underset(r=7)overset(10)sum""^(10)C_(r)(0.9)^(r)(0.1)^(10-r)`
Promotional Banner

Topper's Solved these Questions

  • PROBABILITY II

    CENGAGE PUBLICATION|Exercise SOLVED EXAMPLES|21 Videos

  • PROBABILITY II

    CENGAGE PUBLICATION|Exercise CONCEPT APPCICATION EXERCISE 14.1|5 Videos

  • PROBABILITY I

    CENGAGE PUBLICATION|Exercise JEE Advanced|7 Videos

  • PROGRESSION AND SERIES

    CENGAGE PUBLICATION|Exercise ARCHIVES (NUMERICAL VALUE TYPE )|8 Videos

Similar Questions

Explore conceptually related problems

It is known that 10% of certain articles manufactured are defective. What is the probability that in a random sample of 12 such articles, 9 are defective?

There are 5% defective items in a large bulk of items. What is the probability that a sample of 10 items will include not more than one defective item?

25% of the inhabitnts in a large town are bespectacled. What is the probability that a randomly selected group of 6 inhabitants will include at most 2 bespectacled pesons?

In a certain population, 10% of the people are rich, 5% are famous, and 3% are rich and famous. Then find the probability that a person picked at random from the population is either famous or rich but not both.

X and Y stand in line at random with 10 other people what is the probability that there are 3 people between X and Y ?

In a city suppose 3% of the population is known to be affected by a particular disease. There is a test for the disease. Of there with the disease 98% test positive and of these without the disease 99.8% test positive. What would be the probability that an individual selected at random with a positive test result does not have the disease?

Suppose that 5% of men and 0.25% of women have grey hair. A grey haired person is selected at random. What is the probability of this person being male? Assume that there are equal number of males and females.

Given four pair of gloves, they are distributed to four persons. Each person is given a right-handed and left-handed glove, then the probability that no person gets a pair is

A survey of people in a given region showed that 20% were smokers. The probablity of death due to lung cancer, given that a person smoked, was 10 times of probability of death due to lung cancer, given that a person did not smoke. If the probability of death due to lung cancer in the ragion is 0.006, what is the probability of death due to lung cancer given that a person is a smoker?

In a certain town, 40% of the people have brown hair, 25% have brown eyes, and 15% have both brown hair and brown eyes. If a person selected at random from the town has brown hair, the probability that he also has brown eyes is 1//5 b. 3//8 c. 1//3 d. 2//3