Probability-Quiz-6

Probability Quiz-6

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. If a party of n persons sit at a round table, then the odds against two specified individual sitting next to each other are:

•  2:(n-3)
•  (n-3):2
•  (n-2):2
•  2:(n-2)

Solution

Q2.The probability that a bulb produced by a factory will fuse after 150 days if used is 0.50. What is the probability that out of 5 such bulbs none will fuse after 150 days of use:

•  1-(19/20)⁵
•  (19/20)⁵
•  (3/4)⁵
•  90(1/4)⁵

Solution

Q3.  A bag contains an assortment of blue and red balls. If two balls are drawn at random, the probability of drawing two red balls if five times the probability of drawing two blue balls.
Furthermore, the probability of drawing one ball of each colour is six times the probability of drawing two blue balls. The number of red and blue balls in the bag is:

•  6, 3
•  3,6
•  2,7
•  None of these

Solution

Q4. Two dices are rolled one after the other. The probability that the number on the first is smaller than the number on the second is:

•  1/2
•  7/18
•  3/4
•  5/12

Solution

Q5. A fair die is tossed repeatedly. A wins if it is 1 or 2 on two consecutive tosses and B wins if it is 3, 4, 5 or 6 on two consecutive tosses. The probability that A wins if the die is tossed indefinitely is:

•  1/3
•  5/21
•  1/4
•  2/5

Solution

Q6. Two numbers x and y are chosen at random (without replacement) from amongst the numbers 1, 2, 3, …, 2004. The probability that x³+y³ is divisible by 3 is:

•  1/3
•  2/3
• 1/6
•  1/4

Solution

Q7. A pair of numbers is picked up randomly (without replacement) from the set {1,2, 3,5, 7, 11, 12, 13, 17, 19}. The probability that the number 11 was picked given that the sum of the numbers was even is nearly:

•  0.1
•  0.125
•  0.24
•  0.18

Solution

Q8. Cards are drawn one-by-one at random from a well-shuffled pack of 52 playing cards until 2 aces are obtained from the first time. The probability that 18 draws are required for this is:

•  3/34
•  17/455
•  561/15925
•  None of these

Solution

Q9. Two numbers a,b are chosen from the set of integers 1,2, 3, …., 39. Then probability that the equation 7a-9b=0 is satisfied is:

•  1/247
•  2/247
•  4/741
•  5/741

Solution

Q10. Words from the letters of the word PROBABILITY are formed by taking all letters at a time. The probability that both B’s are not together and both I’s are not together is:

•  52/55
•  53/55
•  54/55
• None of these

Solution