Probability-Quiz-2

Probability Quiz-2

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. An event X can take place in conjuction with any one of the mutually exclusive and exhaustive events A,B andC. If A,B,C are equiprobable and the probability of X is 5/12, and the probability of X taking place when A has happened is 3/8 while it is 1/4 when B has taken place, then the probability of X taking place in conjuction with C is:

•  5/8
•  3/8
•  5/24
•  None of these

Solution

Q2. If E̅ and F̅ are the complementary events of events E and F, respectively, and if 0 <P(F)<1, then:

•  P(E/F)+P(E̅/F)=1/2
•  P(E/F)+P(E/F̅)=1
•  P(E̅/F)+P(E/F̅)=1
•  P(E/F̅)+P(E̅/F̅)=1

Solution

Q3.  A father has 3 children with at least one boy. The probability that he has 2 boys, and 1 girl is:

•  1/4
•  1/3
•  2/3
•  None of these

Solution

Q4. A pair of unbiased dice is rolled together till a sum of either 5 or 7 is obtained. The probability that 5 comes before 7 is:

•  2/5
•  3/5
•  4/5
•  None of these

Solution

Q5. A 2n digit number starts with 2 and all its digits are prime, then the probability that the sum of all 2 consecutive digits of the number is prime is:

•  4X2³ⁿ
•  4X2^-3n
•  2³ⁿ
•  None of these

Solution

Q6. A coin is tossed 7 times. Then the probability that at least 4 consecutive heads appear is:

•  3/16
•  5/32
• 3/16
•  1/8

Solution

Q7. A speaks truth in 60% cases and B speaks truth in 70% cases. The probability that they will say the same thing while describing a single even is:

•  0.56
•  0.54
•  0.38
•  0.94

Solution

 

Q8.A box contains 2 block, 4 white and 3 red balls. One ball is drawn at random from the box and kept aside. From the remaining balls in the box, another ball is drawn at random and kept aside the first. This process is repeated till all the balls are drawn from the box. The probability that the balls drawn are in the sequence of 2 black, 4 white and 3 red is:

•  1/1260
•  1/7560
•  1/126
•  None of these

Solution

Q9. If a is an integer lying in [-5,30], then the probability that the graph of y=x²+2(a+4)x-5a+64 is strictly above the x-axis is:

•  1/36
•  7/36
•  2/9
•  3/5

Solution

Q10. Twelve balls are distributed among three boxes. The probability that the first box contains three balls is:

•  (110/9)X(2/3)¹⁰
•  (9/100)X(2/3)¹⁰
•  (¹²c₃/122³)X2⁹
• ¹²c₃/3¹²

Solution