Probability Quiz-12

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 car is parked among N cars standing in a row, but not at either end. On his return, the owner finds that exactly ‘r’ of the N palces are still occupied. The probability that the places neighouring his car are empty is:
  •  (r-1)!/(N-1)!
  •  (r-1)!(N-r)!/(N-1)!
  •  ((N-r)(N-r-1))/((N+1)(N+2))
  •  N-rc2/N-1c2

Q2. If three square are selected at random from chessboard, then the probability that they form the letter ‘L’ is:
  •  196/64c3
  •  49/64c3
  •  36/64c3
  •  98/64c3

Q3.  Three houses are available in a locality. Three persons apply for the houses. Each applies for one houses without consulting others. The probability that all three apply for the same houses is:
  •  1/9
  •  2/9
  •  7/9
  •  8/9

Q4. One ticket is selected at random from 100 tickets numbered 00, 01, 02, …, 99. Suppose A and B are the sum and product of the digit found on the ticket. Then P((A=7)/(B=0)) is given by:
  •  2/13
  •  2/19
  •  1/50
  •  None of these

Q5. A doctor is called to see a sick child. The doctor knows (prior to the visit) that 90% of the sick children in that neighborhood are sick with the flu, denoted by F, while 10% are sick with the measles, denoted by M. A well-known symptom of measles is a rash, denoted by R. The probability of having a rash for a child sick with the measles is 0.95. however, occasionally children with the flu also develop a rash, with conditional children with the flu also develop a rash, with conditional probability 0.08. Upon examination the child, the doctor finds a rash. Then what is the probability that the child has the measles?
  •  91/165
  •  90/163
  •  82/161
  •  95/167

Q6. An artillery may be either at point I with probability 8/9 or at point II with probability 1/9. We have 55 shells, each of which can be fired either rat point I or II. Each shell may hit the target, independent of the other shells, with probability 1/2. Maximum number of shells must be fired at point I to have maximum probability is:
  •  20
  •  25
  • 29
  •  35

Q7. An urn contains 3 red balls and n white balls. Mr. A draws two balls together from the urn. The probability that they have the same colour is 1/2.Mr. B draws one balls form the urn, notes its colour and replaces it. He then draws a second ball from the urn and finds that both balls have the same colour is 5/8. The possible value of n is:
  •  9
  •  6
  •  5
  •  1

Q8.Let E be an event which is neither a certainty nor an impossibility. If probability is such that P(E)=1+λ+λ2 and P(E' )=(1+λ)2 in terms of an unknown λ. Then P(E) is equal to:
  •  1
  •  3/4
  •  1/4
  •  None of these

Q9.There are 3 bags which are known to contain 2 white and 3 black, 4 white and 1 black, and 3 white and 7 black balls, respectively. A ball is drawn at random from one of the bags and found to be a black ball. Then the probability that it was drawn from the bag containing the most black ball is:
  •  7/15
  •  5/19
  •  3/4
  •  None of these

Q10. Thirty-two players ranked 1 to 32 are playing in a knockout tournament. Assume that in every match between any two players, the better-ranked player wins, the probability the ranked 2 players are winner and runner up, respectively, is:
  •  16/31
  •  1/2
  •  17/31
  • None of these

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