Probability · JEE Main previous year questions

2017 4 questions

1. Q182017 · 9 Apr 2017 · Shift 1

   From a group of 10 men and 5 women, four member committees are to be formed each of which must contain at least one woman. Then the probability for these committees to have more women than men, is :

   1. A.$\frac{21}{220}$
   2. B.$\frac{3}{11}$
   3. C.$\frac{1}{11}$
   4. D.$\frac{2}{23}$
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   Answer: C

2. Q192017 · 9 Apr 2017 · Shift 1

   Let E and F be two independent events. The probability that both E and F happen is $\frac{1}{12}$ and the probability that neither E nor F happens is $\frac{1}{2}$, then a value of $\frac{P(E)}{P(F)}$ is :

   1. A.$\frac{4}{3}$
   2. B.$\frac{3}{2}$
   3. C.$\frac{1}{3}$
   4. D.$\frac{5}{12}$
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   Answer: A

3. Q212017 · 8 Apr 2017 · Shift 1

   Three persons P, Q and R independently try to hit a target. I the probabilities of their hitting the target are $\frac{3}{4}$, $\frac{1}{2}$ and $\frac{5}{8}$ respectively, then the probability that the target is hit by P or Q but not by R is :

   1. A.$\frac{21}{64}$
   2. B.$\frac{9}{64}$
   3. C.$\frac{15}{64}$
   4. D.$\frac{39}{64}$
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   Answer: A

4. Q222017 · 8 Apr 2017 · Shift 1

   An unbiased coin is tossed eight times. The probability of obtaining at least one head and at least one tail is :

   1. A.$\frac{255}{256}$
   2. B.$\frac{127}{128}$
   3. C.$\frac{63}{64}$
   4. D.$\frac{1}{2}$
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   Answer: B