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- Question
- From 4 children, 2 women and 4 men, 4 person are selected. The probability that there are exactly 2 children among the selected persons, is
Options- A. 11/21
- B. 9/21
- C. 10/21
- D. 5/21
- Correct Answer
- 9/21
ExplanationTotal number of cases = 10c4
Favorable number of cases = 4c2. 6c2
{Since, we are to select 2 children out of 4 and remaining 2 persons are to be selected from remaining 6 persons ( 2W + 4M)}
? required Probability = 4c2 . 6c2 / 10c4
= [{(4 x 3) / (2 x 1)} x {(6 x 5) / (2 x 1)}] / [ (10 x 9 x 8 x 7) / (4 x 3 x 2 x 1)]
= [(12/2) x (30/2)] / 210
= 90 / 210
= 9 /12 - 1. The probability that a leap year selected at random contains 53 Sundays, is
Options- A. 7/366
- B. 26/183
- C. 1/7
- D. 2/7 Discuss
- 2. A speaks truth in 60% of the cases and B in 80% of the cases. In what percentage of cases are they likely to contradict each other, narrating the same incident?
Options- A. 70%
- B. 36%
- C. 22%
- D. 44% Discuss
- 3. Two dice and two coins are tossed. The probability that both the coins show head and the sum of the numbers found on the two dice is a prime number is?
Options- A. 5/72
- B. 1/12
- C. 13/144
- D. 5/48 Discuss
- 4. If n integer taken at random are multiplied together then the probability that the last digit of the product is 2, 4, 6, 8 is?
Options- A. 2n/5n
- B. 4n - 2n / 5n
- C. 4n/5n
- D. 8n - 4n / 5n Discuss
- 5. If the integer m and n are chosen at random between 1 and 100, then the probability that a number of the from 7 m + 7 n is divisible by 5 equals?
Options- A. 1/4
- B. 1/7
- C. 1/8
- D. 1/49 Discuss
- 6. The probability that a man can hit a target is 3/4. He tries 5 times. The probability that he will hit the target atleast three times, is
Options- A. 291/364
- B. 371/464
- C. 471/502
- D. 459/512 Discuss
- 7. A dice is rolled three times and sum of three numbers appearing on the uppermost face is 15. The chance that the first roll was four is
Options- A. 2/5
- B. 1/5
- C. 1/6
- D. None of these Discuss
- 8. If a 4- digit number is formed at random using the digit 1, 3, 5, 7 and 9 without repetition, then the probability that it is divisible by 5, is
Options- A. 4/5
- B. 3/5
- C. 1/5
- D. 2/3 Discuss
- 9. If three marbles are picked at random, what is the probability that at least one is blue?
Options- A. 7/12
- B. 37/44
- C. 5/12
- D. 7/44 Discuss
- 10. If 56P r + 6 : 54P r + 3 = 30800 : 1 then the value of r is?
Options- A. 40
- B. 41
- C. 42
- D. None of these Discuss
Probability problems
Search Results
Correct Answer: 2/7
Explanation:
In a leap year, there are 366 days. It means 52 full weeks + 2 odd days. These two days can be (Mon, Tues), (Tues, Wed), (Wed, Thurs), (Thurs, Fri), (Fri, Sat), (Sat, Sun) or (Sun, Mon),
So, Required probability = 2/7
Correct Answer: 44%
Explanation:
Let A = Event that A speaks the truth
and B = Event that B speaks the truth
Then, P(A) = 60/100 = 3/5 and P(A) = 80/100 = 4/5
? P(A) = (1 - 3/5) = 2/5 and
P(B) = (1 - 4/5) = 1/5
P(A and B contradict each other)
= P [(A speaks the truth and B tells a lie) or (A tells a lie and B speak the truth)]
=P[(A and B) or (A and B)]
=P(A and B) + P (A and B)
= P(A) x P(B) + P(A) x P(B)
= (3/5 x 1/5) + ( 2/5 x 4/5)
= (3/25 + 8/25 ) = 11/25
= (11/25 x 100)% = 44%
Correct Answer: 5/48
Explanation:
The probability that head is show in one coin is 1/2.
The probability that the sum of the number on the dice is a prime = the probability that the following pair of number on the dice is a getting on the dice, namely (1, 1), (1, 2), (2, 1), (1, 4 ), (4, 1), (2, 3), (3, 2), (1, 6), (6, 1), (2, 5), (5, 2), (3, 4), (4, 3), (6, 5), (5, 6) = 15/36.
? The required probability = 1/2 x 1/2 x 15/36 = 5/48.
Correct Answer: 4n - 2n / 5n
Explanation:
If the last digit in the product is to 2, 4, 6, 8 the last digit in all the n number should not be 0 and 5 and the last digit of all number should not be selected exclusively from the set of number {1, 3, 7, 9}
? Favourable number of cases
= 8n - 4n
But generally the last digit can be one of 0, 1, 2, 3, .... 9.
Hence, the total number of ways = 10n
Hence, the required probability
= 8n - 4n / 10n
= 4n - 2n / 5n
Correct Answer: 1/8
Explanation:
Number of possible cases = 100 x 100 for 7m + 7n to be divisible by 5,
One of the term has to end with 9 and other with 1 (7m cannot be divided by 9 )
? m can be 2, 6 , 10, 14, ..... 98 (25 values) and n can be 4, 8, 12 ...... 100(25 values)
Since m and n can interchange
? Required probability = (2 x 25 x 25) / (100 x 100) = 1/8
Correct Answer: 459/512
Explanation:
Required Probability
Given, n = 5 and r = 3
Then, Success P = 3/4
Failure, q = 1 - 3/4 = 1/4
Man hit the target thrice
= 5c3 (3/4)3 (1/4)2 + 5c4 (3/4)3 (1/4) + 5c3(3/4)5
= (270/1024) + (405/1024) + (243/1024)
= 918/1024
= 459/512
Correct Answer: None of these
Explanation:
Total number of favourable outcomes n(S) = 63 = 216
Combinations of outcomes for getting sum of 15 on uppermost face = (4, 5, 6), (5, 4, 6), ( 6, 5, 4), (5, 6, 4), (4, 6, 5), (6, 4, 5), (5, 5, 5),(6, 6, 3), (6, 3, 6), (3, 6, 6)
Now, outcomes on which first roll was a four, n(E) = (4, 5, 6),(4, 6, 5)
? P(E) = n(E)/n(S) = 2/216 =1/108
Correct Answer: 1/5
Explanation:
Number of 4- digit numbers which are formed with 1, 3, 5, 7, 9 = 5P4
= 5 x 4 x 3 x 2 = 120 = n (s)
Number of 4 digit number which are formed with 1, 3, 5, 7, 9 and are divisible by 5 = 4P3
= 4 x 3 x 2 = 24 = n (E)
? p(E) = n(E)/n( s) = 24/120
= 1/5
Correct Answer: 37/44
Explanation:
Total number of possible outcomes
= 12C3 = 220
Number of events which do not contain blue marbles (3 marbles out of 7 marbles) = 7C3 = 35
? Required probability = 1 - 35/220 = 37/44
Correct Answer: 41
Explanation:
? 56Pr + 6 : 54Pr + 3 = 30800 : 1
? 56! / (50 - r)! = (30800 x 54!) / (51-r!)
? 56 x 55 = 30800/(51 - r)
? 51 - r = 10
? r = 41
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