Introduction to Mathematical Modelling

  • Question 1
    CBSEENMA9003987

    In a cricket match, a batswoman hits a boundary 6 times out of 30 balls she plays. Find the probability that she did not hit a boundary.

    Solution

    Let E be the event of hitting the boundary.

    Then,
    straight P left parenthesis straight E right parenthesis equals fraction numerator his space the space boundary over denominator Total end fraction equals 6 over 30 equals 1 half equals 0.2

    ∴ Probability of not hitting the boundary
    = 1 – Probability of hitting the boundary
    = 1 – P(E) = 1 – 0.2 = 0.8.


    Question 2
    CBSEENMA9003988

    1500 families with 2 children were selected randomly, and the following data were recorded:

    Number of girls in a family

    2

    1

    0

    Number of families

    475

    814

    211

    Compute the probability of a family, chosen at random, having

    (0 2 girls (ii) 1 girl (iii) No girl.

    Also check whether the sum of these probabilities is 1.

    Solution

    Total number of families
    = 475 + 814 + 211 = 1500
    (i) Probability of a family, chosen at random,
    having 2 girls = 475 over 1500 equals 19 over 60
    (ii) Probability of a family, chosen at random,
    having 1 girl  equals 814 over 1500 equals 407 over 750
    (iii) Probability of a family, chosen at random,
    having no girl  equals 211 over 1500
    Sum of these probabilities
    equals 19 over 60 plus 407 over 750 plus 211 over 1500
equals fraction numerator 475 plus 814 plus 211 over denominator 1500 end fraction equals 1500 over 1500 equals 1
    Hence, the sum is checked.

    Question 3
    CBSEENMA9003989

    In a particular section of Class IX, 40 students were asked about the months of their birth, the following graph was prepared for the data so obtained. Find the probability that a student of the class was bom in August.


    Solution

    Total number of students bom in the year =3+4+2+2+5+1+2+6+3+4+4+4=40
    Number of students bom in August = 6
    ∴ Probability that a student of the class was
    born in August = 6 over 40 equals 3 over 20.

    Question 4
    CBSEENMA9003990

    Three coins are tossed simultaneously 200 times with the following frequencies of different outcomes:

    Outcome

    3 heads

    2 heads

    1 head

    No head

    Frequency

    23

    72

    71

    28

    If the three coins are simultaneously tossed again, compute the probability of 2 heads coming up.

    Solution

    Total number of times the three coins are tossed = 200
    Number of times when 2 heads appear = 72
    ∴ Probability of 2 heads coming up
    equals 72 over 200 equals 9 over 25.

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