Probability Quiz-17

Dear Readers,

Probability is an important topic in JEE advanced examination. In this exam, probability carries weightage of 7% of questions. With focused practice good marks can be fetched from this topic .

Q1. A JEE aspirant estimates that she will be successful with an 80% chance if she studies 10 hours per day, with a 60% chance if she studies 7 hours per day and with a 40% chance if she studies 4 hours per day. She further believes that she will study 10 hours, 7 hours and 4 hours per day with probabilities 0.1, 0.2 and 0.7, respectively
The chance she will be successful is:
  •  0.28
  •  0.38
  •  0.48
  •  0.58

Q2.Let S and T are two events defined on a sample space with probabilities P(S)=0.5,P(T)=0.69,P(S/T)=0.5
Events S and T are:
  •  Mutually exclusive
  •  Independent
  •  Mutually exclusive and independent
  •  Neither mutually exclusive nor independent

Q3.  An amoeba either splits into two or remains the same or eventually dies out immediately after completion of every second with probabilities, respectively,1/2, 1/4 and ¼. Let the initial amoeba if it is distinct from the previous one, be called as 2^nd,3^rd,… generations
The probability that immediately after completion of 2s all the amoeba population dies out is:
  •  9/32
  •  11/32
  •  1/2
  •  3/32

Q4. A cube having all of its sides painted is cut by two horizontal, two vertical and other two planes so as to form 27 cubes all having the same dimensions. Of these cubes, a cube is selected at random
The probability that the cube selected has none of its sides painted is:
  •  1/9
  •  1/27
  •  1/18
  •  5/54

Q5.There are some experiments in which the outcomes cannot be identified discretely. For example, an ellipse of eccentricity 2√2/3 is inscribed in a circle and a point within the circle is chosen at random. Now, we want to find the probability that this point lies outside the ellipse. Then, the point must lie in the shaded region shown in figure. Let the radius of the circle be a and length of minor axis of the ellipse be 2b. Given that 1-b2/a2 =8/9⇒b2/a2 =1/9.

Then, the area of circle serves as sample space and area of the shaded region represents the area for favourable cases. Then, required probability is p=(area of shaded region)/(area of circle) =(πa2-πab)/(πa2 ) =1-b/a =1-b/a =1-1/3 =2/3
Now answer the following question.
A point is selected at random inside a circle. The probability that the point is closer to the centre of the circle than to its circumference is:

  •  1/4
  •  1/2
  •  1/3
  •  1/√2

Q6. If the squares of a 8×8 chessboard are painted either red or black at random
The probability that not all the squares in any column are alternating in colour is:
  •  (1-1/27)8
  •  1/256
  • 1-1/27
  •  None of these

Q7. Two fair dice are rolled. Let P(Ai )>0 denote the event that the sum of the faces of the dice is divided by i
Which one of the following events is most probable?
  •  A3
  •  A4
  •  A5
  •  A6

Q8.A player tosses a coin and scores one point for every head and two points for every tail that turns up. He plays on until his score reaches or passes n.P_n denotes the probability of getting a score of exactly n
The value of Pn is equal to:
  •  (1/2)[P(n-1)+P(n-2))]
  •  (1/2)[2P(n-1)+P(n-2))]
  •  (1/2)[P(n-1)+2P(n-2))]
  •  None of these

Q9.The probability that a family has exactly n children is ap^n,n≥1. All sex distributions of n children in a family have the same probability
The probability that a family contains exactly k boys is (where k≥1):
  •  αpk (1-p)(-k-1)
  •  2αpk (2-p)(-k-1)
  •  2αpk (2-p)(-k)
  •  2αpk-1 (2-p)(-k-1)

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