Probability · JEE Main previous year questions

2018 4 questions

1. Q212018 · 16 Apr 2018 · Shift 1

   Let A, B and C be three events, which are pair-wise independent and $\overline{E}$ denotes the complement of an event E. If $P(A\cap B\cap C)=0$ and $P(C)>0$, then $P\left[\left(\overline{A}\cap \overline{B}\right)|C\right]$ is equal to :

   1. A.$P\left(\overline{A}\right)-P(B)$
   2. B.$P(A)+P\left(\overline{B}\right)$
   3. C.$P\left(\overline{A}\right)-P\left(\overline{B}\right)$
   4. D.$P\left(\overline{A}\right)+P\left(\overline{B}\right)$
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   Answer: A

2. Q222018 · 16 Apr 2018 · Shift 1

   Two different families A and B are blessed with equal number of children. There are 3 tickets to be distributed amongst the children of these families so that no child gets more than one ticket. If the probability that all the tickets go to the children of the family B is $\frac{1}{12}$, then the number of children in each family is :

   1. A.3
   2. B.4
   3. C.5
   4. D.6
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   Answer: C

3. Q212018 · 15 Apr 2018 · Shift 1

   A box 'A' contains 2 white, 3 red and 2 black balls. Another box 'B' contains 4 white, 2 red and 3 black balls. If two balls are drawn at random, without replacement, from a randomly selected box and one ball turns out to be white while the other ball turns out to be red, then the probability that both balls are drawn from box 'B' is :

   1. A.$\frac{9}{16}$
   2. B.$\frac{7}{16}$
   3. C.$\frac{9}{32}$
   4. D.$\frac{7}{8}$
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   Answer: B

4. Q182018 · 8 Apr 2018 · Shift 1

   A bag contains 4 red and 6 black balls. A ball is drawn at random from the bag, its colour is observed and this ball along with two additional balls of the same colour are returned to the bag. If now a ball is drawn at random from the bag, then the probability that this drawn ball is red, is :

   1. A.$\frac{3}{4}$
   2. B.$\frac{3}{10}$
   3. C.$\frac{2}{5}$
   4. D.$\frac{1}{5}$
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   Answer: C