# Question 5 - Examples - Chapter 13 Class 12 Probability

Last updated at April 16, 2024 by Teachoo

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Chapter 13 Class 12 Probability

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Last updated at April 16, 2024 by Teachoo

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(0.1 , ๐๐ ๐ฅ=0@๐๐ฅ, ๐๐ ๐ฅ=1 ๐๐ 2@๐(5โ๐ฅ), ๐๐ ๐ฅ=3 ๐๐ 4@0, ๐๐กโ๐๐๐ค๐๐ ๐)โค (a) Find the value of kMaking in tabular foArmat Since X is a random variable , its Sum of Probabilities is equal to 1 โ_0^4โใ๐(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 โฅ 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 โค 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