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.**In the random experiment of tossing two unbiased dice let E be the event of getting the sum 8 and F be the event of getting even numbers on both the dice. Then,

Statement 1: P(E)=7/36

Statement 2: P(F)=1/3

**Q2.**Four numbers are chosen at random (without replacement) from the set {1, 2, 3,………, 20}

Statement 1: The probability that the chosen numbers when arranged in some order will form an AP,is 1/85

Statement 2: If the four chosen numbers form an AP, then the set of all possible values of common difference is {±1,±2,±3,±4,±5}

**Q3.**Statement 1: If A and B are two events such that 0<P(A),P(B)<1, then P(A/A̅)+P(A̅/B̅)=3/2

Statement 2: If A and B are two events such that 0<P(A),P(B)<1, then P(A/B)=P(A∩B)/P(B) and P(B̅)=P(A∩B̅)+P(A̅∩B̅)

**Q4.**Consider an event for which probability of success is 1/2

Statement 1: Probability that in n trials, there are r success where r=4k and k is an integer is 1/4+1/2

^{(n/2+1)}cos(nÏ€/4)

Statement 2:

^{n}c

_{0}+

^{n}c

_{4}+

^{n}c

_{8}...=2

^{(n/2)}sin(nÏ€/4)

**Q5.**Let A and B be two events such that P(A)=3/5and P(B)=2/3. Then

Statement 1: 4/15≤P(A∩B)≤3/5

Statement 2: 2/5≤P(A/∩B)≤9/10

**Q6.**Statement 1: A natural number x is chosen at random from the first 100 natural numbers. The probability that ((x-10)(x-50))/(x-30)>0 is 0.69.

Statement 2: If A is an event, then O<P(A)<1.

**Q7.**Statement 1: If 12 coins are thrown simultaneously, then probability of appearing exactly five head is equal to probability of appearing exactly 7 heads.

Statement 2:

^{n}c

_{r}=

^{n}c

_{r}⇒either r=s or r+s=n and P(H)=P(T) in a single trial.

**Q8.**Statement 1: If A={2,4,6},B={1,2,3} where A and B are the events of numbers occurring on a dice, then P(A)+P(B)=1

Statement 2: If A

_{1},A

_{2},A

_{3},…,A

_{n}are all mutually exclusive events, then P(A

_{1})+P(A

_{2})+...+P(A

_{n})=1

**Q9.**Statement 1: Out of 5 tickets consecutively numbered three are drawn at random. The chance that the numbers on them are in A.P. is 2/15

Statement 2: Out of 2n+1 tickets consecutively numbered, three are drawn at random, the chance that the numbers on them are in A.P. is 3n/(4n

^{2}-1)

**Q10.**Let A,B and C be three events associated to a random experiment

Statement 1: If A∩B⊆C, then P(C)≥P(A)+P(B)-1

Statement 2: If P{(A∩B)∪(B∩C)∪(C∩A)} ≤min〖{P(A∪B),P(B∪C),P(C∪A)}〗