Sign in
12thPass logo
New chatPYQ LibraryDoubtsRank report
Sign in to see Recents

Your guest activity stays on this device

Sign in to save progress →
Sign in

Probability question

2008 · Shift 0 · Q33
Guest · filters and generic practice availableBrowsing as a guest · PYQ filters and generic practice are available. Sign in only for personalised features and saved progress.
  1. PYQ Library
  2. /JEE Main
  3. /Mathematics
  4. /Probability
  5. /2008 · Shift 0 · Q33

Probability question

2008 · Shift 0 · Q33

JEE MainMathematicsProbabilityMCQ+4 / −1
A die is thrown. Let AAA be the event that the number obtained is greater than 3.3.3. Let BBB be the event that the number obtained is less than 5.5.5. Then P(A∪B)P\left( {A \cup B} \right)P(A∪B) is :
  1. A
    35{3 \over 5}53​
  2. B
    000
  3. C
    111
  4. D
    25{2 \over 5}52​
View written solutionFree

Correct answer: C

  1. Sample space of a die

A fair die has outcomes: S={1,2,3,4,5,6}S=\{1,2,3,4,5,6\}S={1,2,3,4,5,6}

  1. Define the events

  • Event AAA: number obtained is greater than 333 A={4,5,6}A=\{4,5,6\}A={4,5,6}

  • Event BBB: number obtained is less than 555 B={1,2,3,4}B=\{1,2,3,4\}B={1,2,3,4}

  1. Find A∪BA\cup BA∪B

The union means outcomes that are in AAA or in BBB (or both): A∪B={4,5,6}∪{1,2,3,4}={1,2,3,4,5,6}=SA\cup B=\{4,5,6\}\cup\{1,2,3,4\}=\{1,2,3,4,5,6\}=SA∪B={4,5,6}∪{1,2,3,4}={1,2,3,4,5,6}=S

So, A∪BA\cup BA∪B is the entire sample space.

  1. Compute the probability

Since A∪B=SA\cup B=SA∪B=S, P(A∪B)=P(S)=1P(A\cup B)=P(S)=1P(A∪B)=P(S)=1

  1. Check options
  • A: 35\frac{3}{5}53​ ❌
  • B: 000 ❌
  • C: 111 ✅
  • D: 25\frac{2}{5}52​ ❌

Therefore, the correct answer is: 1\boxed{1}1​ which corresponds to Option C.

PreviousNext

More from Probability

  • It is given that the events A and B are such that P(A)=41​,P(A∣B)=21​ and P(B∣A)=32​. Then P(B) is :2008 · MCQ
  • Two aeroplanes I and II bomb a target in succession. The probabilities of I and II scoring a hit correctly are 0.3 and 0.2, respectively. The second plane will bomb only if the first misses…2007 · MCQ
  • At a telephone enquiry system the number of phone cells regarding relevant enquiry follow Poisson distribution with an average of 5 phone calls during 10 minute time intervals. The probability that there is at the most one phone call…2006 · MCQ
  • Three houses are available in a locality. Three persons apply for the houses. Each applies for one house without consulting others. The probability that all the three apply for the same house is :2005 · MCQ
  • A random variable X has Poisson distribution with mean 2. Then P(X>1.5) equals :2005 · MCQ
  • Let A and B two events such that P(A∪B)=61​,P(A∩B)=41​ and P(A)=41​, where A stands for complement of…2005 · MCQ
  • The probability that A speaks truth is 54​, while the probability for B is 43​. The probability that they contradict each other when asked to speak on a fact is :2004 · MCQ
  • Five horses are in a race. Mr. A selects two of the horses at random and bets on them. The probability that Mr. A selected the winning horse is :2003 · MCQ