A box contains 90 discs which are numbered from 1 to 90. If one disc is drawn at random from the box, find the probability that it bears

Question

A box contains 90 discs which are numbered from 1 to 90. If one disc is drawn at random from the box, find the probability that it bears
(i) a two-digit number
(ii) a perfect square number
(iii) a number divisible by 5.
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Amelia 2 weeks 2021-10-14T01:17:35+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-10-14T01:19:11+00:00

    \huge\boxed{\fcolorbox{white}{pink}{Answer}}

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    The total numbers of discs = 50

    P(E) = (Number of favourable outcomes/ Total number of outcomes)

    (i) Total number of discs having two digit numbers = 81

    (Since 1 to 9 are single digit numbers and so, total 2 digit numbers are 90 – 9 = 81)

    P (bearing a two-digit number) = 81/90 = 9/10 = 0.9

    (ii) Total number of perfect square numbers = 9 (1, 4, 9, 16, 25, 36, 49, 64 and 81)

    P (getting a perfect square number) = 9/90 = 1/10 = 0.1

    (iii) Total numbers which are divisible by 5 = 18 (5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85 and 90)

    P (getting a number divisible by 5) = 18/90 = ⅕ = 0.2

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    0
    2021-10-14T01:19:15+00:00

    Answer :

    • Total outcome for every part is same = 90

    1.

    • There are 81 two digits number from 1 to 90 so possible outcomes are 81

    \sf{\boxed{\red{Probability = \dfrac{Favourable\:Outcome}{Total\:Outcome}}}}

    \sf{Probability = \dfrac{81}{90}}

    So , probability of getting a two digit number is \sf\dfrac{81}{90}

    2.

    • There are 9 perfect square till 90 . So, the possibile outcomes are 9.

    \sf{\boxed{\red{Probability = \dfrac{Favourable\:Outcome}{Total\:Outcome}}}}

    \sf{Probability = \dfrac{9}{90}}

    So , probability of getting a perfect Square number is \sf\dfrac{1}{10}

    3.

    • There are 18 number between 1 and 90 which are divisible by 5 so possible outcomes are 5

    \sf{\boxed{\red{Probability = \dfrac{Favourable\:Outcome}{Total\:Outcome}}}}

    \sf{Probability = \dfrac{5}{90}}

    \sf{Probability = \dfrac{1}{18}}

    So , probability of getting a two digit number is \sf\dfrac{1}{18}

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