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There is a Hockey match of Dhyanchand tomorrow, at Motera stadium. In recent years, it has rained only 73 days each year. Unfortunately, the weatherman has predicted rain for tomorrow. When it actually rains, the weatherman correctly forecasts rain 80 of the time. When it doesn't rain, he incorrectly forecasts rain 20 of the time. What is the probability that it will rain on the day of Dhyanchand's Hockey match?
  • a)
    5
  • b)
    3
  • c)
    2
  • d)
    1
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
There is a Hockey match of Dhyanchand tomorrow, at Motera stadium. In...
The sample space is defined by two mutually-exclusive events - it rains or it does not rain. Additionally, a third event occurs when the weatherman predicts rain. Notation for these events appears below.
Event A1 It rains on Dhyanchand's Hockey match.
Event A2 It does not rain on Dhyanchand's Hockey match Event B The weatherman predicts rain.
In terms of probabilities, we know the following:
P (A1) = 73/365 = 0.2 [It rains 73 days out of the year.]
P (A2) = 292/365 = 0.8 [It does not rain 292 days out of the year.]
P (B|A1) = 0.8 [When it rains, the weatherman predicts rain 80% of the time.] P (B|A2) = 0.2 [When it does not rain, the weatherman predicts rain 20% of the time.] We want to know P (A1|B), the probability it will rain on the day of Dhyanchand's Hockey match, given a forecast for rain by the weatherman. The answer can be determined from Bayes' theorem, as shown below.
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Most Upvoted Answer
There is a Hockey match of Dhyanchand tomorrow, at Motera stadium. In...
Given Information:
- Probability of rain on a day in recent years = 73/365 = 0.2
- Probability of correct rain forecast when it actually rains = 0.8
- Probability of incorrect rain forecast when it doesn't rain = 0.2

Calculating the Probability of Rain on the Day of the Hockey Match:
- Let R be the event that it rains on the day of the Hockey match
- Let F be the event that the weatherman forecasts rain
- We need to find P(R), the probability that it will rain on the day of the Hockey match

Using Bayes' Theorem:
- P(R|F) = P(F|R) * P(R) / [P(F|R) * P(R) + P(F|¬R) * P(¬R)]
- P(R|F) = 0.8 * 0.2 / [0.8 * 0.2 + 0.2 * 0.8] = 0.16 / 0.32 = 0.5

Answer:
Therefore, the probability that it will rain on the day of Dhyanchand's Hockey match is 0.5, which is option (c) 2.
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There is a Hockey match of Dhyanchand tomorrow, at Motera stadium. In recent years, it has rained only 73 days each year. Unfortunately, the weatherman has predicted rain for tomorrow. When it actually rains, the weatherman correctly forecasts rain 80 of the time. When it doesn't rain, he incorrectly forecasts rain 20 of the time. What is the probability that it will rain on the day of Dhyanchand's Hockey match?a) 5b) 3c) 2d) 1Correct answer is option 'C'. Can you explain this answer?
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