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03 Aug 2021, 01:30
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The following table shows the contents of a bag containing a variety of objects.
If three objects are drawn at random from the bag, then what is the probability that at least one of them is red?
A. 3/17
B. 45/136
C. 7/17
D. 14/17
E. 149/170
2020-09-07_17-53-17.png [ 20.46 KiB | Viewed 2566 times ]
If three objects are drawn at random from the bag, then what is the probability that at least one of them is red?
A. 3/17
B. 45/136
C. 7/17
D. 14/17
E. 149/170
Attachment:
2020-09-07_17-53-17.png [ 20.46 KiB | Viewed 2566 times ]
03 Aug 2021, 01:40
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Explanation:
total objects = 17
Red objects = 7
Non Red Objects = 17 - 7 = 10
Probability of no red in 3 draws = 10/17 * 9/16 * 8/15
= 3/17
Probability of at least one red = 1 - 3/17 = 14/17
IMO-D
total objects = 17
Red objects = 7
Non Red Objects = 17 - 7 = 10
Probability of no red in 3 draws = 10/17 * 9/16 * 8/15
= 3/17
Probability of at least one red = 1 - 3/17 = 14/17
IMO-D
asishron29181
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03 Aug 2021, 03:20
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Total items: 17
Non red items = 10
Probability of selecting atleast one red item = 1 - Probability of selecting none red items
Total ways of selecting = 17 C 3 = 17*16*15 / 3*2*1 = 680
Total ways of selecting none red items = 10C3 = 10*9*8 / 3*2 = 120
Required probability = (1 - 120/ 680 )
= 14/17
IMO D
Non red items = 10
Probability of selecting atleast one red item = 1 - Probability of selecting none red items
Total ways of selecting = 17 C 3 = 17*16*15 / 3*2*1 = 680
Total ways of selecting none red items = 10C3 = 10*9*8 / 3*2 = 120
Required probability = (1 - 120/ 680 )
= 14/17
IMO D
