Probability Quiz-15
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. 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
Statement 1: P(E)=7/36
Statement 2: P(F)=1/3
Solution
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}
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}
Solution
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)
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)
Solution
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(nπ/4)
Statement 2: nc0+nc4+nc8...=2(n/2) sin(nπ/4)
Solution
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
Statement 1: 4/15≤P(A∩B)≤3/5
Statement 2: 2/5≤P(A/∩B)≤9/10
Solution
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.
Statement 2: If A is an event, then O<P(A)<1.
Solution
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: ncr=ncr⇒either r=s or r+s=n and P(H)=P(T) in a single trial.
Statement 2: ncr=ncr⇒either r=s or r+s=n and P(H)=P(T) in a single trial.
Solution
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 A1,A2,A3,…,An are all mutually exclusive events, then P(A1 )+P(A2 )+...+P(An )=1
Statement 2: If A1,A2,A3,…,An are all mutually exclusive events, then P(A1 )+P(A2 )+...+P(An )=1
Solution
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/(4n2-1)
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/(4n2-1)
Solution
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)}〗
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)}〗
Solution
