NCERT Class 11-Math's: Exemplar Chapter –16 Probability Part 4

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Question 6:

Probability that a truck stopped at a roadblock will have faulty brakes or badly worn tires are and , respectively. Also, the probability is that a truck stopped at the roadblock will have faulty brakes and/or badly working tires. What is the probability that a truck stopped at this roadblock will have faulty brakes as well as badly worn tires?

Answer:

Let B be the event that a truck stopped at the roadblock will have faulty brakes and T be the event that it will have badly worn tires. We have and

and

So

Question 7:

If a person visits his dentist, suppose the probability that he will have his teeth cleaned is , the probability that he will have a cavity filled is , the probability that he will have a tooth extracted is , the probability that he will have a teeth cleaned and a cavity filled is , the probability that he will have his teeth cleaned and a tooth extracted is , the probability that he will have a cavity filled and a tooth extracted is , and the probability that he will have his teeth cleaned, a cavity filled, and a tooth extracted is . What is the probability that a person visiting his dentist will have atleast one of these things done to him?

Answer:

Let C be the event that the person will have his teeth cleaned and F and E be the event of getting cavity filled or tooth extracted, respectively. We are given

,

Now,

Long Answer Type

Question 8:

An urn contains twenty white slips of paper numbered from 1 through 20, ten red slips of paper numbered from 1 through 10, forty yellow slips of paper numbered from 1 through 40, and ten blue slips of paper numbered from 1 through 10. If these 80 slips of paper are thoroughly shuffled so that each slip has the same probability of being drawn. Find the probabilities of drawing a slip of paper that is

(a) Blue or white

(b) Numbered or

(c) Red or yellow and numbered or

(d) Numbered , or ;

(e) White and numbered higher than or yellow and numbered higher than .

Answer:

(a)

(b)

(c)

(d)

(e) P(White and numbered higher than or Yellow and numbered higher than 26)