AIEEE Sample Problems : Statistics and Probability

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List of Sample Problems

1. Question 1: Two numbers are chosen at random from the set {1,2,3,4,5,6}, one after the other, without replacement. What is the probability that the sum of the two numbers is divisible by 3?
   1. 4/5
   2. 1/5
   3. 4/15
   4. 1/3
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2. Question 2: An urn contains 27 black balls and 26 white balls. Players A and B play a game which goes like this. Each of them alternately picks 2 balls from the urn - if both the balls are black, they are replaced with 2 white balls, if both are white then they are just removed from the urn, and if there is one black and 1 white ball, it is replaced with one black ball. This process is repeated until there is only one ball remaining in the urn. Player A wins if the ball remaining is white, player B wins if the remaining ball is black. What is the probability of player A winning the game?
   1. 1
   2. 0
   3. 26/53
   4. Cannot be computed with given information
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3. Question 3: 6 people A, B, C, D, E, F play a game. Each person rolls a 6-faced die once, starting from A first and ending with F with the 6th and last roll of dice. A wins the game if he rolls 1 during his throw, B wins the game if he rolls either 1 or 2 (of course if A has not won the game by then), C wins if he rolls either a 1, 2 or 3 and so on. Who is most likely to win this game?
   1. B
   2. B or C
   3. C
   4. A or F
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4. Question 4: If A and B are two events, then P(A U B) _________
   1. is not less than P(A) + P(B) - 1
   2. is not less than P(A) and P(B)
   3. is equal to P(A) if B is a subset of A
   4. is equal to P(A) + P(B) - P(A) * P(B)
      
      
   1. All 4 are true
   2. a, b and c are true
   3. b, c and d are true
   4. b and c are true
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5. Question 5:A and B are two events, Probability of at least one of them occurring is 0.7, probability of both occurring at the same time is 0.1. If both are independent events, P(A) can be _______
   1. 0.2
   2. 0.4
   3. 0.3
   4. Cannot say
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AIEEE Math Problems, Practice Questions and Answers : Listed Topicwise