A box contains four red balls and two white balls. A trialconsists of mixing up
ID: 2913659 • Letter: A
Question
A box contains four red balls and two white balls. A trialconsists of mixing up the balls, selecting a ball at random, notingits color and then returning it to the box. So: 1) What is the probability of obtaining a red ball in onetrial? 2) For two trials, find the probability that a red ball iselected on the first trial and a white ball is selected on thesecond trial. 3) For two trials, find the probability that a white ball isselected in the first trial and a red ball in the secondtrial. 4) For two trials, find that probability that the number ofred balls selected is one. 5) For three trials, find the probability that two red ballsare selected. 6) For three trials, find the probability that the number ofred balls selected is not greater than two. A box contains four red balls and two white balls. A trialconsists of mixing up the balls, selecting a ball at random, notingits color and then returning it to the box. So: 1) What is the probability of obtaining a red ball in onetrial? 2) For two trials, find the probability that a red ball iselected on the first trial and a white ball is selected on thesecond trial. 3) For two trials, find the probability that a white ball isselected in the first trial and a red ball in the secondtrial. 4) For two trials, find that probability that the number ofred balls selected is one. 5) For three trials, find the probability that two red ballsare selected. 6) For three trials, find the probability that the number ofred balls selected is not greater than two.Explanation / Answer
The problem involves replacement, in which probabilities for agiven event are generally fixed. The probability of picking awhite ball is 1/3. The probability of picking a red ball is2/3. 1) Probability of selecting a red ball is the basicprobability of selecting a red ball - 2/3 2) Probability of red ball * Probability of white ball = 2/3* 1/3. However, there are two ways this may be done. Thus, we must divide by two! 1/9. 3) Three is just two with the order reversed. However, as youare multiplying, the answers are the same. Wonderfulproperties of this set of numbers! 1/9 4) Probability of red ball * Probability of not red ball (whiteball) = 2/3 * 1/3 = 2/9. This time, as order does not matter,the answer is 2/9. 5) Probability of red ball * Probability of red ball * Probabilityof not red ball = 2/3 * 2/3 * 1/3 = 4/27. Order doesnot matter. 6) Not greater than two? In this case, it is easier to findthe complement, probability that all selected are white. Probability of white * Probability of white * Probability of white= 1/3 * 1/3 * 1/3 = 1/27. However, we want the opposite ofthat so subtract it from 1! Answer is 26/27.
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