| A number is chosen at random among the first 100 natural numbers. Find the probability of the number chosen to be a multiple of 7. |
A) \[\frac{3}{50}\]
B) \[\frac{7}{50}\]
C) \[\frac{11}{50}\]
D) \[\frac{9}{50}\]
Correct Answer: B
Solution :
| Total number of ways of selecting one number from 100 numbers is \[{}^{100}{{C}_{1}},\]ways. Let E be the event of drawing a multiple of 7. Then, |
| \[E=\{7,\]\[14,\]\[21,\]\[28,\]\[35,\]\[42,\]\[49,\]\[56,\]\[63,\]\[70,\]\[77,\]\[84,\]\[91,\]\[98\}\] |
| \[\therefore \]\[P\,\,(E)=\frac{n\,\,(E)}{n\,\,(S)}=\frac{14}{{}^{100}{{C}_{1}}}=\frac{14}{100}=\frac{7}{50}\] |
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