## Probability Quiz-1

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. The probability that a marksman will hit a target is given as 1/5. Then the probability that at least once hit in 10 shots is:
•  1-(4/5)10
•  1/510
•  1-(1/5)10
•  (4/5)10
Solution

Q2. In a certain town, 40% of the people have brown hair, 25% have brown eyes and 15% have both brown hair and brown eyes. If a person selected at random from the town, has brown hair, the probability that he also has brown eyes is
•  1/5
•  3/8
•  1/3
•  2/3
Solution

Q3.  Let A and B be two events such that P((A̅⩂B̅))=1/6.P(A⋂B)=1/4 and P(A̅)=1/4where A̅ stands for complement of event A. Then events A and B are:
•  Equally likely but not independent
•  Equally likely and mutually exclusive
•  Mutually exclusive and independent
•  Independent but not equally likely
Solution

Q4. There are 10 prizes, five A’s, there B’s and two C’s, placed in identical sealed envelopers for the top 10 contestants in a mathematics contest. The prizes are awarded by allowing winners to select an envelope at random from those remaining. When the 8^th contestant goes to select the prize, the probability that the remaining three prizes are one A, one B and one C is:
•  1/4
•  1/3
•  1/12
•  1/10
Solution

Q5. One mapping is selected at random from all mappings of the set S={1,2,3,…,n} into itself. If the probability that the mapping is one-one is 3/32, then the value of n is:
•  2
•  3
•  4
•  None of these
Solution

Q6.  In a n-sided regular polygon, the probability that the two diagonal chosen at random will intersect inside the polygon is:
•  2nc2/(nc2−2)c2
•  n(n-1)c2/(nc2−n)c2
• nc4/(nc2−2)c2
•  None of these
Solution

Q7. A bag contains 20 coins. If the probability that the bag contains exactly 4 biased coin is 1/3 and that of exactly 5 biased coin is 2/3, then the probability that all the biased coin are sorted out from the bag in exactly 10 draws is:
•  5/10 X(16c6/20c9)+1/10 X(15c5/20c9)
•  2/33[(16c6+515c5)/20c9
•  5/33 X(16c6/20c9)+1/11 X(15c5/20c9)
•  None of these
Solution

Q8. An unbiased coin is tossed 6 times. The probability that third head appears on the sixth trial is:
•  5/16
•  5/32
•  5/8
•  5/64
Solution

Q9. If n integers taken at random are multiplied together, then the probability that the last digit of the product is 1, 3, 7 or 9 is:
•  2n/5n
•  4n-2n/5n
•  4n/5n
•  None of these
Solution

Q10. A four figure number is formed of the figures 1, 2, 3, 5 with no repetitions. The probability that the number is divided by 5 is:
•  3/4
•  1/4
•  1/8
• None of these
Solution

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