Chapter 11: Problem 18
Use the fact that we have independent events \(\mathrm{A}\) and \(\mathrm{B}\) with \(P(A)=0.7\) and \(P(B)=0.6\). Find \(P(A\) or \(B)\).
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In Exercises \(\mathrm{P} .78\) to \(\mathrm{P} .81,\) use the probability function given in the table to calculate: (a) The mean of the random variable (b) The standard deviation of the random variable $$ \begin{array}{lcccc} \hline x & 10 & 12 & 14 & 16 \\ \hline p(x) & 0.25 & 0.25 & 0.25 & 0.25 \\ \hline \end{array} $$
Find the specified areas for a \(N(0,1)\) density. (a) The area above \(z=-2.10\) (b) The area below \(z=-0.5\) (c) The area between \(z=-1.5\) and \(z=0.5\)
State whether the two events (A and B) described are disjoint, independent, and/or complements. (It is possible that the two events fall into more than one of the three categories, or none of them.) South Africa plays Australia for the championship in the Rugby World Cup. At the same time, Poland plays Russia for the World Team Chess Championship. Let \(\mathrm{A}\) be the event that Australia wins their rugby match and \(\mathrm{B}\) be the event that Poland wins their chess match.
Find endpoint(s) on a \(N(0,1)\) density with the given property. P.137 (a) The area to the left of the endpoint is about 0.10 (b) The area to the right of the endpoint is about 0.80 (c) The area between \(\pm z\) is about 0.95 .
Use the information that, for events \(\mathrm{A}\) and \(\mathrm{B},\) we have \(P(A)=0.4, P(B)=0.3,\) and \(P(A\) and \(B)=0.1.\) Find \(P(A\) or \(B).\)
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