Engineering Maths - Probability

16. Let Let A and B be two events defined as

Let A and B be two events defined as

Let A and B be two events defined as

Then P (A ∩ B) will be

  • Option : A
  • Explanation : A ∩ B = φ

    P (A ∩ B) = 0

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18. What is the probability of correctly choosing an unknown integer between 0 to 9 within three chances?

  • Option : B
  • Explanation : S = [0, 1, 2, ....,9)
    Suppose we want a particular integer "3" to be
    chosen.
    9
    Probability of not choosing "3" is 9/10 (in one
    chance)
    Probability of not choosing 3 in all the three
    chances

                         Probability

    Hence probability of choosing it in at least one
    of the three chances

                Probability

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19. A five figure number is formed by the digits 0, 1,2,3,4 without repetition. Then the probability that the number formed is divisible by 4 is

  • Option : B
  • Explanation : The five digits can be arranged in 5! ways, out
    of which 4! will begin with zero.

    Total number of 5-figure numbers formed
                         = 5! - 4! = 96.
    Those numbers formed will be divisible by 4
    which will have two extreme right digits
    divisible by 4,
    i.e., numbers ending in 04, 12,20,24,32,40.
    Now, numbers ending in 04 = 3! = 6,
    numbers ending in 12 = 3! - 2! = 4,
    numbers ending in 20 = 3! = 6,
    numbers ending in 24 = 3! - 2! = 4,
    numbers ending in 32 = 3! - 2! = 4,
    and numbers ending in 40 = 3! = 6.
    [Numbers having 12, 24, 32 in the extreme right
    are (3! - 2!), since the numbers having zero on
    t.he extreme left are to excluded.]
    Total number of favourable ways
    6 + 4 + 6 + 4 + 4 + 6 = 30
    Hence,    required probability = Probability

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20. A bag contains 8 white and 6 red balls. The probability of drawing two balls of the same colour is

  • Option : B
  • Explanation : Two balls out 14 can be drawn in 14C2 ways which is the total number of outcomes.

    Two white balls out of 8 can he drawn in 8C2 ways

    Probability of drawing 2 white balls

                                                              Probability

    Similarly 2 red balls out of 6 call be drawn in
    6C2 ways

                                                                Probability
    Probability of drawing 2 red balls
    Probability of drawing 2 balls of the same
    colour (either both white or both red)

      Probability

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