Example 5 - The record of a weather station shows that - Examples

  1. Chapter 15 Class 9 Probability
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Example 5 The record of a weather station shows that out of the past 250 consecutive days, its weather forecasts were correct 175 times. (i) What is the probability that on a given day it was correct? The total number of days for which the record is available = 250 Number of days when forecast was correct = 175 P(the forecast was correct on a given day) = (๐‘๐‘ข๐‘š๐‘๐‘’๐‘Ÿ ๐‘œ๐‘“ ๐‘‘๐‘Ž๐‘ฆ๐‘  ๐‘“๐‘œ๐‘Ÿ ๐‘คโ„Ž๐‘’๐‘› ๐‘“๐‘œ๐‘Ÿ๐‘’๐‘๐‘Ž๐‘ ๐‘ก ๐‘ค๐‘Ž๐‘  ๐‘๐‘œ๐‘Ÿ๐‘Ÿ๐‘’๐‘๐‘ก)/(๐‘‡๐‘œ๐‘ก๐‘Ž๐‘™ ๐‘›๐‘ข๐‘š๐‘๐‘’๐‘Ÿ ๐‘œ๐‘“ ๐‘‘๐‘Ž๐‘ฆ๐‘  ๐‘“๐‘œ๐‘Ÿ ๐‘คโ„Ž๐‘–๐‘โ„Ž ๐‘กโ„Ž๐‘’ ๐‘Ÿ๐‘’๐‘๐‘œ๐‘Ÿ๐‘‘ ๐‘–๐‘  ๐‘Ž๐‘ฃ๐‘Ž๐‘–๐‘™๐‘Ž๐‘๐‘™๐‘’) = 175/250 = 0.7 Example 5 (Method 1) The record of a weather station shows that out of the past 250 consecutive days, its weather forecasts were correct 175 times. (ii) What is the probability that it was not correct on a given day? The total number of days for which the record is available = 250 The number of days when the forecast was not correct = 250 โ€“ 175 = 75 P(the forecast was not correct on a given day) = (๐‘๐‘ข๐‘š๐‘๐‘’๐‘Ÿ ๐‘œ๐‘“ ๐‘‘๐‘Ž๐‘ฆ๐‘  ๐‘“๐‘œ๐‘Ÿ ๐‘คโ„Ž๐‘’๐‘› ๐‘“๐‘œ๐‘Ÿ๐‘’๐‘๐‘Ž๐‘ ๐‘ก ๐‘ค๐‘Ž๐‘  ๐‘›๐‘œ๐‘ก ๐‘๐‘œ๐‘Ÿ๐‘Ÿ๐‘’๐‘๐‘ก)/(๐‘‡๐‘œ๐‘ก๐‘Ž๐‘™ ๐‘›๐‘ข๐‘š๐‘๐‘’๐‘Ÿ ๐‘œ๐‘“ ๐‘‘๐‘Ž๐‘ฆ๐‘  ๐‘“๐‘œ๐‘Ÿ ๐‘คโ„Ž๐‘–๐‘โ„Ž ๐‘กโ„Ž๐‘’ ๐‘Ÿ๐‘’๐‘๐‘œ๐‘Ÿ๐‘‘ ๐‘–๐‘  ๐‘Ž๐‘ฃ๐‘Ž๐‘–๐‘™๐‘Ž๐‘๐‘™๐‘’) = 75/250 = 0.3 Example 5 (Method 2) The record of a weather station shows that out of the past 250 consecutive days, its weather forecasts were correct 175 times. (ii) What is the probability that it was not correct on a given day? P(the forecast was not correct on a given day) = 1 โ€“ P(forecast was correct on a given day) = 1 โ€“ 0.7 = 0.3

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.
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