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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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During the \(2010-11\) NBA season, Ray Allen of the Boston Celtics had a free throw shooting percentage of \(0.881 .\) Assume that the probability Ray Allen makes any given free throw is fixed at 0.881 , and that free throws are independent. (a) If Ray Allen shoots two free throws, what is the probability that he makes both of them? (b) If Ray Allen shoots two free throws, what is the probability that he misses both of them? (c) If Ray Allen shoots two free throws, what is the probability that he makes exactly one of them?
State whether the process described is a discrete random variable, is a continuous random variable, or is not a random variable. Deal cards one at a time from a deck. Keep going until you deal an ace. Stop and count the total number of cards dealt.
The most common form of color blindness is an inability to distinguish red from green. However, this particular form of color blindness is much more common in men than in women (this is because the genes corresponding to the red and green receptors are located on the X-chromosome). Approximately \(7 \%\) of American men and \(0.4 \%\) of American women are red-green color-blind. \(^{6}\) (a) If an American male is selected at random, what is the probability that he is red-green color-blind? (b) If an American female is selected at random, what is the probability that she is NOT redgreen color-blind? (c) If one man and one woman are selected at random, what is the probability that neither are red-green color-blind? (d) If one man and one woman are selected at random, what is the probability that at least one of them is red-green color-blind?
Is the Stock Market Independent? The Standard and Poor 500 (S\&P 500 ) is a weighted average of the stocks for 500 large companies in the United States. It is commonly used as a measure of the overall performance of the US stock market. Between January 1,2009 and January \(1,2012,\) the S\&P 500 increased for 423 of the 756 days that the stock market was open. We will investigate whether changes to the S\&P 500 are independent from day to day. This is important, because if changes are not independent, we should be able to use the performance on the current day to help predict performance on the next day. (a) What is the probability that the S\&P 500 increased on a randomly selected market day between January 1,2009 and January \(1,2012 ?\) (b) If we assume that daily changes to the \(\mathrm{S} \& \mathrm{P}\) 500 are independent, what is the probability that the S\&P 500 increases for two consecutive days? What is the probability that the S\&P 500 increases on a day, given that it increased the day before? (c) Between January 1,2009 and January 1,2012 the S\&P 500 increased on two consecutive market days 234 times out of a possible 755 . Based on this information, what is the probability that the S\&P 500 increases for two consecutive days? What is the probability that the \(\mathrm{S} \& \mathrm{P}\) 500 increases on a day, given that it increased the day before? (d) Compare your answers to part (b) and part (c). Do you think that this analysis proves that daily changes to the S\&P 500 are not independent?
Determine whether the process describes a binomial random variable. If it is binomial, give values for \(n\) and \(p .\) If it is not binomial, state why not. Worldwide, the proportion of babies who are boys is about \(0.51 .\) We randomly sample 100 babies born and count the number of boys.
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