Question 5 - Examples - Chapter 13 Class 12 Probability

Last updated at Dec. 16, 2024 by

Example 26 Let X denote the number of hours you study during a randoml

Example 26 - Chapter 13 Class 12 Probability - Part 2
Example 26 - Chapter 13 Class 12 Probability - Part 3
Example 26 - Chapter 13 Class 12 Probability - Part 4

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Question 5 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 Question 5 (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 has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo