SolveItClass 10 · NCERT

NCERT Solutions · Class 10 Mathematics Probability

25 questions · 25 still being checked

EXERCISE 14.1 21–25 (part 3 of 3)

  1. Exercise 21

    A lot consists of 144\displaystyle 144 ball pens of which 20\displaystyle 20 are defective and the others are good. Nuri will buy a pen if it is good, but will not buy if it is defective. The shopkeeper draws one pen at random and gives it to her. What is the probability that
    (i)
    She will buy it ?
    (ii)
    She will not buy it ?
    NCERT’s answer
    (i)
    $\displaystyle \frac{31}{36}$ (ii) $\displaystyle \frac{5}{36}$

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  2. Exercise 22

    Refer to Example 13.
    (i)
    Complete the following table:
    Event: 'Sum on 2\displaystyle 2 dice'2\displaystyle 23\displaystyle 34\displaystyle 45\displaystyle 56\displaystyle 67\displaystyle 78\displaystyle 89\displaystyle 910\displaystyle 1011\displaystyle 1112\displaystyle 12
    Probability136\displaystyle \frac{1}{36}536\displaystyle \frac{5}{36}136\displaystyle \frac{1}{36}
    (ii)
    A student argues that 'there are 11\displaystyle 11 possible outcomes 2\displaystyle 2, 3\displaystyle 3, 4\displaystyle 4, 5\displaystyle 5, 6\displaystyle 6, 7\displaystyle 7, 8\displaystyle 8, 9\displaystyle 9, 10\displaystyle 10, 11\displaystyle 11 and 12. Therefore, each of them has a probability 111\displaystyle \frac{1}{11}. Do you agree with this argument? Justify your answer.
    NCERT’s answer
    (i)
    Sum on $\displaystyle 2$ dice$\displaystyle 2$$\displaystyle 3$$\displaystyle 4$$\displaystyle 5$$\displaystyle 6$$\displaystyle 7$$\displaystyle 8$$\displaystyle 9$$\displaystyle 10$$\displaystyle 11$$\displaystyle 12$
    Probability$\displaystyle \frac{1}{36}$$\displaystyle \frac{2}{36}$$\displaystyle \frac{3}{36}$$\displaystyle \frac{4}{36}$$\displaystyle \frac{5}{36}$$\displaystyle \frac{6}{36}$$\displaystyle \frac{5}{36}$$\displaystyle \frac{4}{36}$$\displaystyle \frac{3}{36}$$\displaystyle \frac{2}{36}$$\displaystyle \frac{1}{36}$
    (ii) No. The eleven sums are not equally likely.

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  3. Exercise 23

    A game consists of tossing a one rupee coin 3\displaystyle 3 times and noting its outcome each time. Hanif wins if all the tosses give the same result i.e., three heads or three tails, and loses otherwise. Calculate the probability that Hanif will lose the game.
    NCERT’s answer
    $\displaystyle \frac{3}{4}$; Possible outcomes are : HHH, TTT, HHT, HTH, HTT, THH, THT, TTH. Here, THH means tail in the first toss, head on the second toss and head on the third toss and so on.

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  4. Exercise 24

    A die is thrown twice. What is the probability that
    (i)
    5\displaystyle 5 will not come up either time?
    (ii)
    5\displaystyle 5 will come up at least once? [Hint : Throwing a die twice and throwing two dice simultaneously are treated as the same experiment] \footnotetext{ * Not from the examination point of view. }
    NCERT’s answer
    (i)
    $\displaystyle \frac{25}{36}$ (ii) $\displaystyle \frac{11}{36}$

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  5. Exercise 25

    Which of the following arguments are correct and which are not correct? Give reasons for your answer.
    (i)
    If two coins are tossed simultaneously there are three possible outcomes-two heads, two tails or one of each. Therefore, for each of these outcomes, the probability is 13\displaystyle \frac{1}{3}.
    (ii)
    If a die is thrown, there are two possible outcomes-an odd number or an even number. Therefore, the probability of getting an odd number is 12\displaystyle \frac{1}{2}.
    NCERT’s answer
    (i)
    Incorrect. We can classify the outcomes like this but they are not then 'equally likely'. Reason is that 'one of each' can result in two ways - from a head on first coin and tail on the second coin or from a tail on the first coin and head on the second coin. This makes it twicely as likely as two heads (or two tails). (ii) Correct. The two outcomes considered in the question are equally likely. \section*{EXERCISE A1.1}

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