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  1. Chapter 13 Class 12 Probability
  2. Serial order wise

Transcript

Example 26 Let X denote the number of hours you study during a randomly selected school day. The probability that X can take the values x, has the following form, where k is some unknown constant. P(X = x) = {โ–ˆ(0.1 , ๐‘–๐‘“ ๐‘ฅ=0@๐‘˜๐‘ฅ, ๐‘–๐‘“ ๐‘ฅ=1 ๐‘œ๐‘Ÿ 2@๐‘˜(5โˆ’๐‘ฅ), ๐‘–๐‘“ ๐‘ฅ=3 ๐‘œ๐‘Ÿ 4@0, ๐‘œ๐‘กโ„Ž๐‘’๐‘Ÿ๐‘ค๐‘–๐‘ ๐‘’)โ”ค (a) Find the value of kMaking in tabular foArmat Since X is a random variable , its Sum of Probabilities is equal to 1 โˆ‘_0^4โ–’ใ€–๐‘ƒ(๐‘‹)ใ€— = 1 P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 1 0.1 + k + 2k + 2k + k = 1 6k = 1 โ€“ 0.1 6k = 0.9 k = (0. 9)/6 k = 0.15 Example 26 (b) What is the probability that you study atleast two hours? Exactly two hours? At most 2 HoursOur probability distribution table is P(you study atleast two hours) = P(X โ‰ฅ 2) = P(X = 2) + P(X = 3) + P(X = 4) = 2k + 2k + k = 5k = 5 ร— 0.15 = 0.75 P(you study exactly two hours) = P(X = 2) = 2k = 2 ร— 0.15 = 0.30 P(you study atmost two hours) = P(X โ‰ค 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.1 + k + 2k = 0.1 + 3k = 0.1 + 3 ร— 0.15 = 0.1 + 0.45 = 0.55

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.