Engineering Mathematics - Probability and Statistics

Question - 1

There are two containers, with one containing 4 red and 3 green balls and other containing 3 blue and 4 green balls. One ball is drawn at random from each container. The probability that one of the the balls is red and the other is blue will be

  • A 17
  • B \(\frac { 9 }{ 49 } \)
  • C \(\frac { 12 }{ 49 } \)
  • D \(\frac { 3 }{ 7 } \)

Question - 2

Two coins are simultaneously tossed. The probability of two heads simultaneously appearing is

  • A \(\frac { 1 }{ 8 } \)
  • B \(\frac { 1 }{ 6 } \)
  • C \(\frac { 1 }{ 4 } \)
  • D \(\frac { 1 }{ 2 } \)

Question - 3

Three values of x and y are to be fitted in a straight line in the form y=1+bx by the method of least squares. Give \(\sum { x=6, } \sum { y=21, } \sum { { x }^{ 2 } } =14\quad and\quad \sum { xy=46 } \)the value of a and b are respectively

  • A 2 and 3
  • B 1 and 2
  • C 2 and 1
  • D 3 and 2

Question - 4

The standard deviation of spot speed of vehicles in, a highway is 8.8km/h and the mean speed of the vehicles is 33km/h the coefficient of variation in speed is

  • A 0.1517
  • B 0.1867
  • C 0.2666
  • D 0.3646

Question - 5

A hydraulic structure has four gates which operate independently. The probability of failure of each gate is 0.2. Given that gate 1 has failed, the probability that both gates 2 and 3 will fail is

  • A 0.240
  • B 0.200
  • C 0.040
  • D 0.008

Question - 6

If P and Q are two random events, then which of the following is true?

  • A Independence of P and Q implies that probability (P\(\cap \)Q)=0
  • B Probability (P\(\cup \)Q)\(\ge \)Probability (P)+Probability (Q)
  • C If P and Q are mutually exclusive, then they must be independent
  • D Probability (P\(\cap \)Q)\(\le \)Probability (P)

Question - 7

A box contains 4 white balls and 3 red balls. In succession, two balls randomly selected and removed from the box. Given that the first removed ball is white, the probability that the second removed ball is red, is

  • A \(\frac { 1 }{ 3 } \)
  • B \(\frac { 3 }{ 7 } \)
  • C \(\frac { 1 }{ 2 } \)
  • D \(\frac { 4 }{ 7 } \)

Question - 8

Assume for simplicity that N people, all born in April (a month of 30 days) are collected in a room. Consider, the event of atleast two people in the room being born on the same date of the month, even in different years, e.g., 1980 and 1985. What is the smallest N. So that the probability of this event exceeds 0.5?

  • A 20
  • B 7
  • C 15
  • D 16

Question - 9

A loaded dice has following probability distribution of occurrences

Dice value 1 2 3 4 5 6
Probability \(\frac { 1 }{ 4 } \) \(\frac { 1 }{ 8 } \) \(\frac { 1 }{ 8 } \) \(\frac { 1 }{ 8 } \) \(\frac { 1 }{ 8 } \) \(\frac { 1 }{ 4 } \)

If three identical dice as the above are thrown, the probability of occurrence of values 1, 5 and 6 on the three dice is

  • A same as that of occurrence 3, 4, 5
  • B same as that of occurrence 1, 2, 5
  • C \(\frac { 1 }{ 128 } \)
  • D \(\frac { 5 }{ 8 } \)

Question - 10

A fair coin is tossed three times in succession. If the first toss produces a head, then the probability of getting exactly two heads in three tosses is

  • A \(\frac { 1 }{ 8 } \)
  • B \(\frac { 1 }{ 2 } \)
  • C \(\frac { 3 }{ 8 } \)
  • D \(\frac { 3 }{ 4 } \)
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