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

2009 · Shift 1 · Q26
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 Advanced
  3. /Mathematics
  4. /Probability
  5. /2009 · Shift 1 · Q26

Probability question

2009 · Shift 1 · Q26

JEE AdvancedMathematicsProbabilityMCQ+4 / −1
A fair die is tossed repeatedly until a six is obtained. Let X denote the number of tosses required.The probability that X≥3X\ge3X≥3 equals :
  1. A
    125216{{125} \over {216}}216125​
  2. B
    2536{{25} \over {36}}3625​
  3. C
    536{{5} \over {36}}365​
  4. D
    25216{{25} \over {216}}21625​
View written solutionFree

Correct answer: B

  1. Let XXX be the number of tosses required to get the first six.

  2. We need to find: P(X≥3)P(X\ge 3)P(X≥3)

  3. The event X≥3X\ge 3X≥3 means that a six is not obtained in the first two tosses.

  4. Since the die is fair, P(not getting a six in one toss)=56P(\text{not getting a six in one toss})=\frac{5}{6}P(not getting a six in one toss)=65​

  5. The tosses are independent, so P(X≥3)=P(no six in first two tosses)=(56)2P(X\ge 3)=P(\text{no six in first two tosses})=\left(\frac{5}{6}\right)^2P(X≥3)=P(no six in first two tosses)=(65​)2

  6. Therefore, P(X≥3)=2536P(X\ge 3)=\frac{25}{36}P(X≥3)=3625​

  7. Comparing with the options, this is Option B.

PreviousNext

More from Probability

  • A fair die is tossed repeatedly until a six is obtained. Let X denote the number of tosses required.The probability that X = 3 equals2009 · MCQ
  • Consider the system of equations ax+by=0;cx+dy=0, where a,b,c,d ∈{0,1} STATEMENT - 1 : The probability that the system of equations has a unique solution is 83​. and STATEMENT - 2 : The probability…2008 · MCQ
  • An experiment has 10 equally likely outcomes. Let A and B be two non-empty events of the experiment. If A consists of 4 outcomes, the number of outcomes that B must have so that A and B are independent is :2008 · MCQ
  • One Indian and four American men and their wives are to be seated randomly around a circular table. Then the conditional probability that the Indian man is seated adjacent to his wife given that each American man is seated adjacent to his…2007 · MCQ
  • Let H 1​, H 2​, ..., H n​ be mutually exclusive and exhaustive events with P(H i​) > 0, i = 1, 2, ..., n. Let E be any other event with 0 Statement 1 : P(H i​ | E) > P(E | H i​). P(H i​) for i=1,2,...,n. Statement 2 :…2007 · MCQ
  • Let Ec denote the complement of an event E. Let E,F,G be pairwise independent events with P(G)>0 and P(E∩F∩G)=0. Then P(Ec∩Fc∣G) equals2007 · MCQ
  • Three students S1​,S2​, and S3​ are given a problem to solve. Consider the following events: U: At least one of S1​,S2​, and S3​ can solve the problem, V: S1​ can solve the problem, given that neither S2​ nor S3​ can solve…2025 · MCQ
  • A factory has a total of three manufacturing units, M1​,M2​, and M3​, which produce bulbs independent of each other. The units M1​,M2​, and M3​ produce bulbs in the proportions of 2:2:1, respectively. It is known that 20%…2025 · Numerical