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NCERT Exemplar · Class 10 Mathematics Statistics and Probability

96 questions · 96 still being checked

EXERCISE 13.1 21–26 (part 3 of 11)

  1. The number of atheletes who completed the race in less then $\displaystyle 14.6$ seconds is :

    Exercise 21

    A card is drawn from a deck of 52\displaystyle 52 cards. The event E is that card is not an ace of hearts. The number of outcomes favourable to E is
    (A)
    4\displaystyle 4 (B) 13\displaystyle 13
    (C)
    48\displaystyle 48
    (D)
    51\displaystyle 51

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    NCERT’s answer
    (D)
    (D) \(\displaystyle 51\)Only the ace of hearts is excluded from E: \[n(E) = 52 - 1 = 51 \]

  2. Exercise 22

    The probability of getting a bad egg in a lot of 400\displaystyle 400 is 0.035. The number of bad eggs in the lot is
    (A)
    7\displaystyle 7 (B) 14\displaystyle 14
    (C)
    21\displaystyle 21
    (D)
    28\displaystyle 28

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    NCERT’s answer
    (B)
    (B) \(\displaystyle 14\)\[P(\text{bad egg}) = \frac{\text{bad eggs}}{\text{lot size}} \] \[0.035 = \frac{\text{bad eggs}}{400} \] \[\text{bad eggs} = 0.035 \times 400 = 14 \]

  3. Exercise 23

    A girl calculates that the probability of her winning the first prize in a lottery is 0.08. If 6000\displaystyle 6000 tickets are sold, how many tickets has she bought?
    (A)
    40\displaystyle 40
    (B)
    240\displaystyle 240
    (C)
    480\displaystyle 480
    (D)
    750\displaystyle 750

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    NCERT’s answer
    (C)
    (C) \(\displaystyle 480\)\[P(\text{winning}) = \frac{\text{tickets bought}}{\text{tickets sold}} \] \[0.08 = \frac{\text{tickets bought}}{6000} \] \[\text{tickets bought} = 0.08 \times 6000 = 480 \]

  4. Exercise 24

    One ticket is drawn at random from a bag containing tickets numbered 1\displaystyle 1 to 40. The probability that the selected ticket has a number which is a multiple of 5\displaystyle 5 is
    (A)
    15\displaystyle \frac{1}{5}
    (B)
    35\displaystyle \frac{3}{5}
    (C)
    45\displaystyle \frac{4}{5}
    (D)
    13\displaystyle \frac{1}{3}

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    NCERT’s answer
    (A)
    (A) \(\displaystyle \frac{1}{5}\)\[\text{multiples of } 5 \text{ in } 1\text{–}40: 5,10,15,20,25,30,35,40 \] \[n(\text{favourable}) = 8, \quad n(\text{total}) = 40 \] \[P = \frac{8}{40} = \frac{1}{5} \]

  5. Exercise 25

    Someone is asked to take a number from 1\displaystyle 1 to 100. The probability that it is a prime is
    (A)
    15\displaystyle \frac{1}{5}
    (B)
    625\displaystyle \frac{6}{25}
    (C)
    14\displaystyle \frac{1}{4}
    (D)
    1350\displaystyle \frac{13}{50}

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    NCERT’s answer
    (C)
    (C) \(\displaystyle \frac{1}{4}\)\[\text{primes in } 1\text{–}100: 2,3,5,7,\ldots,89,97 \] \[n(\text{favourable}) = 25, \quad n(\text{total}) = 100 \] \[P = \frac{25}{100} = \frac{1}{4} \]

  6. Exercise 26

    A school has five houses A, B, C, D and E. A class has 23\displaystyle 23 students, 4\displaystyle 4 from house A, 8\displaystyle 8 from house B, 5\displaystyle 5 from house C, 2\displaystyle 2 from house D and rest from house E. A single student is selected at random to be the class monitor. The probability that the selected student is not from A, B and C is
    (A)
    423\displaystyle \frac{4}{23}
    (B)
    623\displaystyle \frac{6}{23}
    (C)
    823\displaystyle \frac{8}{23}
    (D)
    1723\displaystyle \frac{17}{23}

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    NCERT’s answer
    (B)
    (B) \(\displaystyle \frac{6}{23}\)\[\text{house } E = 23 - 4 - 8 - 5 - 2 = 4 \] \[\text{not } A,B,C = \text{house } D + \text{house } E = 2 + 4 = 6 \] \[P = \frac{6}{23} \]