Answer to Question #148725 in Statistics and Probability for DANIYAL MASOOD

Question #148725
A number x is selected at random in the interval [-1, 1]. Let the events A={x<0}, B={|x-0.5|<1}, and C=x>0.75. Find P[A intersection B], P[A intersection C], P[AUB],P[AUC] and P[AUBUC].
1
Expert's answer
2020-12-07T09:12:01-0500

The probability of an interval [a, b] , where -1 ≤ a ≤ 1 is "\\frac{1}{2}(b-a)"

"P(B) = P(-0.5, 1) = \\frac{3}{4} \\\\\n\nP(A \\cap B) = P(-0.5, 0) = \\frac{1}{4} \\\\\n\nP(A \\cap C) = P(\\oslash ) = 0 \\\\\n\nP(A \\cup B) = P(-1, 1) = 1 \\\\\n\nP(A \\cup C) = P((-1,0) \\cup (0.75, 1)) = \\frac{5}{8} \\\\\n\nP(A \\cup B \\cup C) = P(-1,1) = 1"


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