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- Question
- The probability that a man aged x years will die in a years is p. The probability that out of n men M1, M2, M3...... Mn each aged n years Mk will die and be the first to die is?
Options- A. 1/n2
- B. 1 - (1 - p)n
- C. 1/n2[1 - (1- p)n
- D. 1/n[1 - (1 - p)n]
- Correct Answer
- 1/n[1 - (1 - p)n]
Explanation? Probability that no man out of n men aged x years will die in a year = (1 - p)n
? Probability that out of n men at least one will die in a year = 1 - (1 - p)n .
When at least one, man dies, any one out of the n men may be the first to die - 1. n books are to be arranged on a self. These include m volumes of a science book (m < n). The probability that in any arrangement, the volumes of science books are in ascending order is?
Options- A. 1/ n!
- B. 1/n-m!
- C. 1/m!
- D. m!/n! Discuss
- 2. If an integer is selected at random from 1 to 100. The probability that it relatively prime to 100 is?
Options- A. 2/5
- B. 61/100
- C. 17/100
- D. 19/100 Discuss
- 3. The number of tosses that have to be made in order that there is 99% probability of getting at least one head is?
Options- A. 5
- B. 7
- C. 6
- D. 8 Discuss
- 4. The probability that a marksman will hit a target is given as 1/5. Then his probability of at least one hit in 10 shots, is?
Options- A. 1 - (4/5)10
- B. 1/ (5)10
- C. 1 - 1/ (5)10
- D. (4/5)10 Discuss
- 5. The probability that a person will hit a target in shooting practice is 0.3 . If he shoots 10 times. Then the probability of his shooting the target is?
Options- A. 1
- B. 1 - (0.7)10
- C. (0.7)10
- D. (0.3)10 Discuss
- 6. If the probability of machine failing during a day is 0.95. The probability of its working for four consecutive days without failing is?
Options- A. 0.00000625
- B. 0.0625
- C. 0.16548375
- D. 0.000625 Discuss
- 7. Seven white balls and three black ball are randomly placed in a row. The probability that no two black balls are placed adjacently equals?
Options- A. 1/2
- B. 7/15
- C. 2/15
- D. 1/3 Discuss
- 8. The probability of occurrence of a multiple of 2 on a dice and multiple of 3 on the other dice . If both are thrown together is?
Options- A. 7/26
- B. 1/3
- C. 71/36
- D. 1/4 Discuss
- 9. Two number are selected randomly from the set S = {1, 2, 3, 4, 5, 6} without replacement one by one. The probability that minimum of the number is less than 4 is?
Options- A. 1/15
- B. 14/15
- C. 1/5
- D. 4/5 Discuss
- 10. A bag contains 5 blue and 4 black balls. Three balls are drawn at random. What is the probability that 2 are blue and 1 is black?
Options- A. 1/3
- B. 2/5
- C. 1/6
- D. None of these Discuss
Probability problems
Search Results
Correct Answer: 1/m!
Explanation:
Corresponding to each arrangement of (n - m) other books, there is a unique arrangement of the m volumes of the science book in ascending order and m! arrangement of the m volumes in random order
&Reqd. Prob = p = 1/m!
Correct Answer: 2/5
Explanation:
From the set of odd number < 100, if we exclude multiples of 5, we get the set of numbers < 100 and relatively prime to 100.
The number of such numbers = 50 - 10 = 40
? Reqd. Probability = 40 / 100 = 2/5
Correct Answer: 7
Explanation:
Corresponding to n tosses, the Probability of getting no head = (1/2)n and,
Therefore, the probability of getting at least one head = 1 - (1/2)n
Now, 1 - (1/2)n ? 99/100
? (1/2)n ? 1/100
? n ? 7
Correct Answer: 1 - (4/5)10
Explanation:
? p = 1/5
? q = 1 - 1/5 = 4/5
The probability that none will hit in 10 shots = (4/5)10
? Reqd. probability = 1 - (4/5)10
Correct Answer: (0.3)10
Explanation:
? Probability in each trial (shooting) = 0.3
? Reqd. probability = (0.3)10
Correct Answer: 0.0625
Explanation:
? Probability of machine failing during a day p = 0.95
? q = Probability of its working during a day = 1 - p = 1 - 0.95 = 0.05
Required probability = q4 = (0.05)4
= 0.00000625
Correct Answer: 7/15
Explanation:
n(S) = 10C7 = 10C3
n(E) = 8C3
? P(E) = n(E)/n(S) = 7/15
Correct Answer: 1/3
Explanation:
Probability of multiple of 2 = 3/6 = 1/2
Probability of multiple of 3 = 2/6 = 1/3
Since there are two dice.
? The required probability = 2 x 1/2 x 1/3 = 1/3
Correct Answer: 4/5
Explanation:
Total no . of cases = 6P2 = 6 x 5 = 30
Non-favourable cases are (4, 5) , (5, 4), (4, 6), (6, 4), (5, 6), (6, 5)
? Probability that event will not happen = 6 /(6 x 5) = 1/5
? Reqd. probability = 1 - 1/5 = 4/5
Correct Answer: 1/6
Explanation:
Let S be the sample space and E be the event of drawing 3 balls out of which 2 are blue and 1 is back .
Then, n (S)= Number of ways of drawing 3 balls out of 9=9c3
= (9 x 8 x 7) / (3 x 2 x 1)
= 84 and
n(E) = Number of ways of drawing 2 balls out of 5 and 1 ball out of 4 .
= 5C2 4C11
= (5 x 4) / (2 x 1) + 4 = 14
? P(E) = n(E)/n(S) = 14/84 = 1/6
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