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- Question
- 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
- Correct Answer
- 4/5
ExplanationTotal 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 - 1. 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
- 2. 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
- 3. 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
- 4. 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] Discuss
- 5. 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
- 6. 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
- 7. A six - faced dice is so biased that is twice as likely to show an even number as an odd number when throw. It is thrown twice. The probability that the sum of two number thrown is even is?
Options- A. 1/12
- B. 1/6
- C. 1/3
- D. 5/9 Discuss
- 8. The probability of occurrence of an event A is 5/9 . The probability of non-occurrence of the event B is 5/11. The probability that at least one of them will occur?
Options- A. 6/11
- B. 5/9
- C. 4/9
- D. 0.8 Discuss
- 9. When two dice are thrown, the probability that the difference of the number on the dice is 2 or 3 is?
Options- A. 7/18
- B. 3/11
- C. 5/18
- D. 1/2 Discuss
- 10. From a set of 17 cards numbered 1, 2, 3 ....... 17 one is drawn at random. The probability that the number is divisible by 3 or 7 is?
Options- A. 2/17
- B. 1/7
- C. 7/17
- D. 10/ 17 Discuss
Probability problems
Search Results
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: 7/15
Explanation:
n(S) = 10C7 = 10C3
n(E) = 8C3
? P(E) = n(E)/n(S) = 7/15
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: 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
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: 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
Correct Answer: 5/9
Explanation:
? Probability for odd = p
? Probability for even = 2p
? p + 2p = 1
? 3p = 1
? p = 1/3
? Probability for odd = 1/3, Probability for even = 2/3.
Sum of two nos. is even means either both are odd or both are even
? Reqd. probability = 1/3 x 1/3 + 2/3 x 2/3 = 1/9 + 4/9 = 5/9
[ ? die is thrown twice ]
Correct Answer: 0.8
Explanation:
? P(A) = 5/9
? P(A) = 1- 5/9 = 4/9
? P(B) = 5/11
? P(B) = 1 - 5/11 = 6/11
Probability that none of them will occur = P(A ? B) = 4/9 x 5/ 11 = 20/99
Hence, Reqd. probability = 1-20/99 = 79//99
= 0.798 which is near 0.8.
Correct Answer: 7/18
Explanation:
The favourable cases are (1, 3), (2, 4) , (3, 5), (4, 6) and (1, 4), (2, 5), (3, 6) and their reversed cases like (3, 1), (4, 2), (5, 3)...
Total number of favourable cases = 2 x 7
? Required Probability P(E) = 14/36 = 7/18
Correct Answer: 7/17
Explanation:
Total number of cases is 17.
? Number divisible by 3 are 3, are 3, 6, 9, 12, 15 (These are 5 in number )
Number divisible by 7 are 7, 14. (These are 2 in number )
There are two favourable number of cases
Total no. of favourable number = 5 + 2
Required probability = 7/17.
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