InterviewSolution
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InterviewSolution
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A box contains 19 balls bearing numbers 1, 2, 3 ..., 19 respectively. A ball is drawn at random from the box. Find the probability that the number on the ball is (i) a prime number (ii) an even number (iii) a number divisible by 3. |
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Answer» (i) Total number of ball bearings = 19 Chances of drawing a prime numbered ball = 9 (They are 2,3,5,7,11,13,17,19) Probability (P) = \(\frac{Number\,of\,favorable\,outcomes}{Total\,number\,of\,outcomes}\) ∴ Probability of drawing a prime numbered ball bearing P(prime ball) = \(\frac{possible\,chances\,of\,drawing\,a\,prime\,numbered\,ball\,bearing}{Total\,number\,of\,ball\,bearings}\) = \(\frac{8}{19}\) (ii) Total number of ball bearings = 19 Chances of drawing an even numbered ball = 9 (They are 2,4,6,8,10,12,14,16,18) Probability (P) = \(\frac{Number\,of\,favorable\,outcomes}{Total\,number\,of\,outcomes}\) ∴ Probability of drawing a prime numbered ball bearing P(prime ball) \(\frac{possible\,chances\,of\,drawing\,a\,prime\,numbered\,ball\,bearing}{Total\,number\,of\,ball\,bearings}\) = \(\frac{9}{19}\) (iii) Total number of ball bearings = 19 Chances of drawing a numbered ball which is divisible by 3 = 6 (They are 3,6,9,12,15,18) Probability (P) = \(\frac{Number\,of\,favorable\,outcomes}{Total\,number\,of\,outcomes}\) ∴ Probability of drawing a numbered ball bearing which is divisible by 3 P(ball divisible by 3) = \(\frac{possible\,chances\,of\,drawing\,a\,numbered\,which\,is\,divisible\,by\,3}{Total\,number\,of\,ball\,bearings}\) = \(\frac{6}{19}\) |
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