Probability problems
- 1. 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 Also asked in: Bank Exams, CAT, Bank Clerk, Bank PO
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
- 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
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
- 3. 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
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!
- 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
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
- 5. 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
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
- 6. 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
Correct Answer: 7/15
Explanation:
n(S) = 10C7 = 10C3
n(E) = 8C3
? P(E) = n(E)/n(S) = 7/15
- 7. 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
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
- 8. 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
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
- 9. 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
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
- 10. 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
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 ]
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