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A person on a trip has a choice between private car and public transport. The probability of using a private car is 0.45. While using the public transport, further choices available are bus and metro, out of which the probability of commuting by a bus is 0.55. In such a situation, the probability (rounded up to two decimals) of using a car, bus and metro, respectively would be
  • a)
    0.45, 0.30 and 0.25 
  • b)
    0.45, 0.25 and 0.30
  • c)
    0.45, 0.55 and 0.00 
  • d)
    0.45, 0.35 and  
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
A person on a trip has a choice between private car and public transpo...
Explanation:

To find the probability of using a car, bus, and metro, we need to consider the different scenarios and calculate their probabilities.

Scenario 1: Using a private car
Given that the probability of using a private car is 0.45, the probability of using a car is 0.45.

Scenario 2: Using public transport
If the person decides to use public transport, there are two options available: bus and metro.

Scenario 2.1: Using a bus
Given that the probability of using a bus is 0.55, the probability of using a bus is 0.45 * 0.55 = 0.2475 (rounded to two decimal places).

Scenario 2.2: Using a metro
Since the person has already decided to use public transport and the only options left are bus and metro, the probability of using a metro is 1 - probability of using a bus = 1 - 0.2475 = 0.7525 (rounded to two decimal places).

Therefore, the probability of using a car, bus, and metro would be:
- Car: 0.45
- Bus: 0.2475 (rounded to two decimal places)
- Metro: 0.7525 (rounded to two decimal places)

Thus, the correct answer is option 'A': 0.45, 0.30, and 0.25.
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Community Answer
A person on a trip has a choice between private car and public transpo...
p(private car) = 0.45
p(bus / public transport) = 0.55 
Since a person has a choice between private car and public transport 
p (public transport)= 1 – p(private car)
= 1 – 0.4 5 = 0.55
p (bus) = p(bus ∩ public transport)
= p(bus | public transport)
× p( public transport)
= 0.55 × 0.55 
= 0.3025 = 0.30
Now p (metro) = 1 – [p(private car) + p(bus)]
= 1 – (0.45 + 0.30) = 0.25
∴ p (private car) = 0.45 
p (bus) = 0.30
and p(metro) = 0.25
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A person on a trip has a choice between private car and public transport. The probability of using a private car is 0.45. While using the public transport, further choices available are bus and metro, out of which the probability of commuting by a bus is 0.55. In such a situation, the probability (rounded up to two decimals) of using a car, bus and metro, respectively would bea)0.45, 0.30 and 0.25b)0.45, 0.25 and 0.30c)0.45, 0.55 and 0.00d)0.45, 0.35 and Correct answer is option 'A'. Can you explain this answer?
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A person on a trip has a choice between private car and public transport. The probability of using a private car is 0.45. While using the public transport, further choices available are bus and metro, out of which the probability of commuting by a bus is 0.55. In such a situation, the probability (rounded up to two decimals) of using a car, bus and metro, respectively would bea)0.45, 0.30 and 0.25b)0.45, 0.25 and 0.30c)0.45, 0.55 and 0.00d)0.45, 0.35 and Correct answer is option 'A'. Can you explain this answer? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about A person on a trip has a choice between private car and public transport. The probability of using a private car is 0.45. While using the public transport, further choices available are bus and metro, out of which the probability of commuting by a bus is 0.55. In such a situation, the probability (rounded up to two decimals) of using a car, bus and metro, respectively would bea)0.45, 0.30 and 0.25b)0.45, 0.25 and 0.30c)0.45, 0.55 and 0.00d)0.45, 0.35 and Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A person on a trip has a choice between private car and public transport. The probability of using a private car is 0.45. While using the public transport, further choices available are bus and metro, out of which the probability of commuting by a bus is 0.55. In such a situation, the probability (rounded up to two decimals) of using a car, bus and metro, respectively would bea)0.45, 0.30 and 0.25b)0.45, 0.25 and 0.30c)0.45, 0.55 and 0.00d)0.45, 0.35 and Correct answer is option 'A'. Can you explain this answer?.
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