1. A five digit number is formed with the digits 0,1,2,3 and 4 without repetition.Find the chance that the number is divisible by 5
A)3/5
B)1/5
C)2/5
D)4/5
E)None of these
Sol. 5 digit number = 5! = 120
Divisible by 5 then the last digit should be 0
Then the remaining position have the possibility = 4! =24
P = (4!/5!) = 24/120 = 1/5.
2. A bag contain 6 white balls and 4 red balls .Three balls are drawn randomly.What is the probability that one ball is red and other 2 are white
A)1/2
B)2/1
C)3/2
D)1/3
E)None of these
Sol. Total no of balls = 6+ 4 = 10
3 balls drawn = 10C3 =(10×9×8)/(3×2×1) =120
one ball is red and other 2 are white = 4C1×6C2
4C1×6C2 =(4×6×5)/(1×2)= 60
Probability = 60/120 = 1/2.
3. A box contain 10 red balls, 7 green balls and 12 blue balls. A ball is drawn at random. What is the probability that the ball drawn is either red or green ?
A)7/29
B)12/29
C)17/29
D)10/29
E)None of these
Sol. Total no of balls =10+7+12 = 29
P(R) =10/29
P(G) = 7/29
P(Either red or green) = 10/29 + 7/29 = 17/29.
4. A dice is thrown twice . What is the probability that at least one of them comes up with number 4
A)12/36
B)11/36
C)1/6
D)11/6
E)None of these
Sol. B) 11/36.
5. From a group of 5 men and 2 women , 2 persons are selected at random. Find the probability that at least one woman is selected ?
A)11/7
B)21/11
C)11/21
D)1/21
E)None of these
Sol. n(S) = 7C2 = (7×6)/(1×2) = 21
n(E) = 2C2+5C1 * 2C1 = 1+11
P = n(E)/n(S) = 11/21.
6. A bag contains 11 red and 5 green balls. Find the probability that 4 balls are red and 3 balls are green when 7 balls are drawn at random.
A)16/52
B)15/52
C)11/52
D)10/52
E)None of these
Sol. n(S) = 16C7 = 11440
n(E) = 11C4 ×5C3 = 330×10 = 3300
P = n(E)/ n(S) = 3300/11440 = 15/52.
7. Four different objects 1,2,3 are distributed at random in four places. What is the probability that none of the objects occupies the place corresponding to its number ?
A)1/6
B)1/3
C)1/2
D)1
E)None of these
Sol. PLACE: 1 2 3 4
Random : 2134 , 2143 , 2314 ,2341 , 2413 ,2431
None of the objects occupies the place of that number = 2143 ,2341,2413
n(S) = 6, n(E) = 3
p = 3/6 = 1/2.
8. A box contain 8 red balls, 6 green balls and 8 blue balls. A ball is drawn at random. What is the probability that the ball drawn is neither red nor green ?
A)10/29
B)2/11
C)11/4
D)4/11
E)None of these
Sol. Total no of balls =8+6+8 = 22
P(B) =8/22
P(neither red nor green) = 8/22 = 4/11.
9. A box contains 5 green , 4 yellow and 3 white marbles. Three marbles are drawn at random. What is the probability that they are not of the same colour ?
A)40/44
B)44/41
C)41/44
D)40/39
E)None of these
Sol. n(E) = 5C3+ 4C3+3C3 = 10+4+1 = 15
n(S) = 12C3 = 220
P = n(E)/ n(S) = 15/220 =3/44
Required probability = 1-3/44 = 41/44.
10. Two dice are thrown simultaneously .What is the probability of getting 2 numbers whose product is even ?
A)3/4
B)4/3
C)1/4
D)1/3
E)None of these
Sol. A) 3/4.
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