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A survey is done on 100 candidates, it was found that each candidate likes to watch either cricket or football or both. The number of candidates like cricket is 55 and the number of candidates like football 75. At random one candidate is selected then find the probability that the selected candidate watches both of the games.
- a)0.3
- b)0.2
- c)0.55
- d)0.75
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
A survey is done on 100 candidates, it was found that each candidate l...
Given:
A survey is done on 100 candidates,
The number of candidates like cricket = 55
The number of candidates like football = 75
Concept used:
Probability of happening an event =
Calculation:
According to the question,
In the above figure,
a = number of candidates who likes to watch only cricket
c = number of candidates who likes to watch only football
b = number of candidates who likes to watch both football and cricket
Now,
The number of candidates like to watch cricket = a + b = 55
The number of candidates like to watch football = b + c = 75
The total number of candidates = a + b + c = 100
Now,
⇒ a + b + c = 100
⇒ 55 + c = 100
⇒ c = 45
Now,
⇒ b + c = 75
⇒ b + 45 = 75
⇒ b = 30
The number of candidates who likes to watch both cricket and football = 30
Now,
The required probability = = 0.3
Therefore, '0.3' is the required answer.
Most Upvoted Answer
A survey is done on 100 candidates, it was found that each candidate l...
Understanding the Problem
To find the probability that a randomly selected candidate watches both cricket and football, we can use the principle of inclusion-exclusion.
Given Data
- Total candidates (n) = 100
- Candidates who like cricket (C) = 55
- Candidates who like football (F) = 75
Applying the Inclusion-Exclusion Principle
We know that:
C + F - Both = Total
Where "Both" is the number of candidates who like both cricket and football.
Calculating the Number of Candidates Watching Both Sports
Using the above formula, we can rearrange it as follows:
Both = C + F - Total
Substituting the values:
Both = 55 + 75 - 100
Both = 130 - 100
Both = 30
Calculating the Probability
The probability (P) that a randomly selected candidate watches both cricket and football can be calculated as follows:
P(Both) = Number of candidates who watch both / Total candidates
P(Both) = 30 / 100
P(Both) = 0.3
Conclusion
The probability that a randomly selected candidate watches both cricket and football is 0.3. Therefore, the correct answer is option 'A'.
To find the probability that a randomly selected candidate watches both cricket and football, we can use the principle of inclusion-exclusion.
Given Data
- Total candidates (n) = 100
- Candidates who like cricket (C) = 55
- Candidates who like football (F) = 75
Applying the Inclusion-Exclusion Principle
We know that:
C + F - Both = Total
Where "Both" is the number of candidates who like both cricket and football.
Calculating the Number of Candidates Watching Both Sports
Using the above formula, we can rearrange it as follows:
Both = C + F - Total
Substituting the values:
Both = 55 + 75 - 100
Both = 130 - 100
Both = 30
Calculating the Probability
The probability (P) that a randomly selected candidate watches both cricket and football can be calculated as follows:
P(Both) = Number of candidates who watch both / Total candidates
P(Both) = 30 / 100
P(Both) = 0.3
Conclusion
The probability that a randomly selected candidate watches both cricket and football is 0.3. Therefore, the correct answer is option 'A'.
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A survey is done on 100 candidates, it was found that each candidate likes to watch either cricket or football or both. The number of candidates like cricket is 55 and the number of candidates like football 75. At random one candidate is selected then find the probability that the selected candidate watches both of the games.a)0.3b)0.2c)0.55d)0.75Correct answer is option 'A'. Can you explain this answer?
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