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

2025 · 24 Jan · Shift 1 · Q37
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. /2025 · 24 Jan · Shift 1 · Q37

Probability question

2025 · 24 Jan · Shift 1 · Q37

JEE MainMathematicsProbabilityMCQ+4 / −1
AAA and BBB alternately throw a pair of dice. A wins if he throws a sum of 5 before BBB throws a sum of 8 , and BBB wins if he throws a sum of 8 before AAA throws a sum of 5 . The probability, that A wins if A makes the first throw, is
  1. A
    819\frac{8}{19}198​
  2. B
    919\frac{9}{19}199​
  3. C
    817\frac{8}{17}178​
  4. D
    917\frac{9}{17}179​
View written solutionFree

Correct answer: B

  1. Find the success probabilities on one throw

For a pair of dice:

  • Sum 555 can occur as (1,4),(2,3),(3,2),(4,1)(1,4),(2,3),(3,2),(4,1)(1,4),(2,3),(3,2),(4,1), i.e. 444 outcomes.
  • Sum 888 can occur as (2,6),(3,5),(4,4),(5,3),(6,2)(2,6),(3,5),(4,4),(5,3),(6,2)(2,6),(3,5),(4,4),(5,3),(6,2), i.e. 555 outcomes.

Hence, P(A gets sum 5)=436=19P(\text{A gets sum }5)=\frac{4}{36}=\frac{1}{9}P(A gets sum 5)=364​=91​ P(B gets sum 8)=536P(\text{B gets sum }8)=\frac{5}{36}P(B gets sum 8)=365​

  1. Set up the probability that A wins

Let PPP be the probability that AAA wins when AAA starts.

A wins in two ways:

  • He gets sum 555 on his first throw: probability 19\frac{1}{9}91​.
  • Or, A fails first, B fails next, and then the situation repeats.

Now, P(A fails on his throw)=1−19=89P(\text{A fails on his throw})=1-\frac{1}{9}=\frac{8}{9}P(A fails on his throw)=1−91​=98​ P(B fails on his throw)=1−536=3136P(\text{B fails on his throw})=1-\frac{5}{36}=\frac{31}{36}P(B fails on his throw)=1−365​=3631​

So, P=19+(89⋅3136)PP=\frac{1}{9}+\left(\frac{8}{9}\cdot \frac{31}{36}\right)PP=91​+(98​⋅3631​)P

  1. Solve the equation

P=19+248324P=19+6281PP=\frac{1}{9}+\frac{248}{324}P=\frac{1}{9}+\frac{62}{81}PP=91​+324248​P=91​+8162​P

Thus, P−6281P=19P-\frac{62}{81}P=\frac{1}{9}P−8162​P=91​ 1981P=19\frac{19}{81}P=\frac{1}{9}8119​P=91​ P=19⋅8119=919P=\frac{1}{9}\cdot \frac{81}{19}=\frac{9}{19}P=91​⋅1981​=199​

  1. Check options

The required probability is 919\boxed{\frac{9}{19}}199​​ which corresponds to Option B.

PreviousNext

More from Probability

  • Let A=[aij​] be a square matrix of order 2 with entries either 0 or 1 . Let E be the event that A is an invertible matrix. Then the probability P(E) is :2025 · MCQ
  • Two number k1​ and k2​ are randomly chosen from the set of natural numbers. Then, the probability that the value of ik1​+ik2​,(i=−1​) is non-zero, equals2025 · MCQ
  • Three defective oranges are accidently mixed with seven good ones and on looking at them, it is not possible to differentiate between them. Two oranges are drawn at random from the lot. If x denote the number of defective oranges, then…2025 · MCQ
  • Bag B1​ contains 6 white and 4 blue balls, Bag B2​ contains 4 white and 6 blue balls, and Bag B3​ contains 5 white and 5 blue balls. One of the bags is selected at random and a ball is drawn from it. If the ball is white, then the…2025 · MCQ
  • Let S be the set of all the words that can be formed by arranging all the letters of the word GARDEN. From the set S, one word is selected at random. The probability that the selected word will NOT have vowels in alphabetical order is:2025 · MCQ
  • Bag 1 contains 4 white balls and 5 black balls, and Bag 2 contains n white balls and 3 black balls. One ball is drawn randomly from Bag 1 and transferred to Bag 2. A ball is then drawn randomly from Bag 2. If the probability, that the ball…2025 · MCQ
  • A bag contains 8 balls, whose colours are either white or black. 4 balls are drawn at random without replacement and it was found that 2 balls are white and other 2 balls are black. The probability that the bag contains equal number of…2024 · MCQ
  • Let Ajay will not appear in JEE exam with probability p=72​, while both Ajay and Vijay will appear in the exam with probability q=51​. Then the probability, that Ajay will appear in the exam and Vijay…2024 · MCQ