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Probability Quiz-11

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. Cards are drawn one by one without replacement from a pack of 52 cards. The probability that 10 cards will precede the first ace is:
  •  241/1456
  •  164/4165
  •  451/884
  •  None of these
Solution

Q2. Forty teams play a tournament. Each team plays every other team just once. Each game result in a win for one team. If each team has a 50% chance of winning each game, the probability that at the end of the tournament, every team has won a different number of games is:
  •  1/780
  •  40!/2780
  •  40!/3780
  •  None of these
Solution

Q3.  2n boys are randomally divided into two subgroups containing n boys each. The probability that the two tallest boys are in different groups is:
  •  n/(2n-1)
  •  (n-1)/(2n-1)
  •  (n-1)/4n2
  •  None of these
Solution

Q4. The probability of solving a question by three students are 1/2, 1/4, 1/6 respectively. Probability of question being solved will be:
  •  33/48
  •  35/48
  •  31/48
  •  37/48
Solution

Q5. A fair coin is tossed 10 times. Then the probability that two heads do not occurs consecutively is:
  •  7/64
  •  1/8
  •  9/16
  •  9/64
Solution

Q6. If A and B each toss three coins. The probability that both get the same number of heads is:
  •  1/9
  •  3/16
  • 5/16
  •  3/8
Solution

Q7. A draws a card from a pack of n cards marked 1,2,…n. The card is replaced in the pack and B draws a card. Then the probability that A draws a higher card than B is:
  •  (n+1)2n
  •  1/2
  •  (n-1)/2n
  •  None of these
Solution

Q8.All the jacks, queens, kings and aces of a regular 52 cards deck are taken out. The 16 cards are thoroughly shuffled and my opponent, a person who always tells the truth, simultaneously draws two cards at random and says, ‘I hold at least one ace’. The probability that he holds two aces is:
  •  2/8
  •  4/9
  •  2/3
  •  1/9
Solution

Q9.The probability of winning a race by three persons A,B and C are 1/2, 1/4, and 1/4, respectively. They run two races. The probability of A winning the second race when B wins the first race is:
  •  1/3
  •  1/2
  •  1/4
  •  2/3
Solution

Q10. A composite number is selected at random from the first 30 natural numbers and it is divided by 5. The probability that there will be a remainder is:
  •  14/19
  •  5/19
  •  5/6
  • 7/15
Solution

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