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The odds in favour of standing first of three students Amit, Vikas and Vivek appearing at an examination are 1 : 2. 2 : 5 and 1 : 7 respectively. What is the probability that either of them will stand first (assume that a tie for the first place is not possible).
- a)168 /178
- b)122/ 168
- c)5 /168
- d)125 /168
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
The odds in favour of standing first of three students Amit, Vikas and...
P (Amit) = 1/3 P (vikas) = 2/7 P (vivek) = 1/8. Required Probability = 1/3 + 2/7 + 1/8 = 125/168.
Most Upvoted Answer
The odds in favour of standing first of three students Amit, Vikas and...
To find the probability that either Amit, Vikas, or Vivek will stand first in the examination, we need to calculate the probabilities for each student and then add them together.
Let's calculate the probability for each student:
1. Amit's probability of standing first is given as 1:2. This means that the odds in favor of Amit standing first are 1, and the odds against it are 2. The total odds are 1+2=3. Therefore, the probability of Amit standing first is 1/3.
2. Vikas's probability of standing first is given as 2:5. This means that the odds in favor of Vikas standing first are 2, and the odds against it are 5. The total odds are 2+5=7. Therefore, the probability of Vikas standing first is 2/7.
3. Vivek's probability of standing first is given as 1:7. This means that the odds in favor of Vivek standing first are 1, and the odds against it are 7. The total odds are 1+7=8. Therefore, the probability of Vivek standing first is 1/8.
Now, to find the probability that either of them will stand first, we need to add the probabilities of Amit, Vikas, and Vivek standing first:
Probability = P(Amit) + P(Vikas) + P(Vivek)
= 1/3 + 2/7 + 1/8
To add these fractions, we need to find a common denominator.
The common denominator of 3, 7, and 8 is 168.
Now, let's convert the fractions to have a denominator of 168:
Probability = (56/168) + (48/168) + (21/168)
= (56 + 48 + 21) / 168
= 125 / 168
Therefore, the probability that either Amit, Vikas, or Vivek will stand first is 125/168.
Hence, the correct answer is option 'D' (125/168).
Let's calculate the probability for each student:
1. Amit's probability of standing first is given as 1:2. This means that the odds in favor of Amit standing first are 1, and the odds against it are 2. The total odds are 1+2=3. Therefore, the probability of Amit standing first is 1/3.
2. Vikas's probability of standing first is given as 2:5. This means that the odds in favor of Vikas standing first are 2, and the odds against it are 5. The total odds are 2+5=7. Therefore, the probability of Vikas standing first is 2/7.
3. Vivek's probability of standing first is given as 1:7. This means that the odds in favor of Vivek standing first are 1, and the odds against it are 7. The total odds are 1+7=8. Therefore, the probability of Vivek standing first is 1/8.
Now, to find the probability that either of them will stand first, we need to add the probabilities of Amit, Vikas, and Vivek standing first:
Probability = P(Amit) + P(Vikas) + P(Vivek)
= 1/3 + 2/7 + 1/8
To add these fractions, we need to find a common denominator.
The common denominator of 3, 7, and 8 is 168.
Now, let's convert the fractions to have a denominator of 168:
Probability = (56/168) + (48/168) + (21/168)
= (56 + 48 + 21) / 168
= 125 / 168
Therefore, the probability that either Amit, Vikas, or Vivek will stand first is 125/168.
Hence, the correct answer is option 'D' (125/168).
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The odds in favour of standing first of three students Amit, Vikas and Vivek appearing at an examination are 1 : 2. 2 : 5 and 1 : 7 respectively. What is the probability that either of them will stand first (assume that a tie for the first place is not possible).a)168 /178b)122/ 168c)5 /168d)125 /168Correct answer is option 'D'. Can you explain this answer?
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