Probability-Quiz-4

Probability Quiz-4

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. A and B play a game of tennis. The situation of the game is as follows; if one scores two consecutive points after a deuce, he wins, if loss of a points is followed by win of a point, it is deuce. The chance of a server to win a point is 2/3. The game is at deuce and Ais serving. Probability that A will win the match is (serves are changed after each game):

•  3/5
•  2/5
•  1/2
•  4/5

Solution

Q2.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 l’s are not together is:

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

Solution

Q3.  Events A and C are independent. If the probabilities relating A,B and C areP(A)=1/5,P(B)=1/6,P(A∩C)=1/20;P(B∪C)=3/8. Then:

•  Events B and C are independent
•  Events B and C mutually exclusive
•  Events B and C bare neither independent nor mutually exclusive
•  Events B and C are equiprobable

Solution

Q4. Whenever horses a,b,c race together, their respective probabilities of winning the race are 0.3, 0.5 and 0.2, respectively. If they race three times the probability that the same horse wins all the three races, and the probability that a,b,c each wins one race are, respectively:

•  8/50, 9/50
•  16/100, 3/100
•  12/50, 15/50
•  10/50, 8/50

Solution

Q5.Given two eventsB. If odds against A are as 2:1 and those in favour of A∪B areas 3:1, then:

•  1/2≤P(B)≤3/4
•  5/12≤P(B)≤3/4
•  1/4≤P(B)≤3/5
•  None of those

Solution

Q6. Two players toss 4 coins each. The probability that they both obtain the same number of heads is:

•  5/256
•  1/16
• 35/128
•  None of these

Solution

Q7. Three integers are chosen at random from the first 20 integers. The probability that their product is even is:

•  2/19
•  3/29
•  17/19
•  4/29

Solution

Q8.A die is rolled 4 times. The probability of getting a larger number than the previous number each time is:

•  17/216
•  5/432
•  15/432
•  None of these

Solution

Q9.A die is thrown a fixed number of times. If probability of getting number 3 times is same as the probability of getting even number 4 times, then probability of getting even number exactly once is:

•  1/6
•  1/9
•  5/36
•  7/128

Solution

Q10. An unbiased cubic die marked with 1, 2, 2, 3, 3, 3 is rolled 3 times. The probability of getting a total score of 4 or 6 is:

•  16/216
•  50/216
•  60/216
• None of these

Solution