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Two random numbers are selected between 0 and 1. What is the probability of getting the second number more than 0.75 given that the first number is less than 0.25?
Wiki User
∙ 13y ago
If the two numbers are chosen randomly, they are independent so the fact that the value of the first is completely irrelevant. The probability that the second is more than 0.75 is the probability that a random number, between 0 and 1, is greater than 0.75 and that probability is 0.25.
The probability would be 1/32. Possible answers that fit the conditions would be .2,1 .2,.95 but .95,2 will not work. what you have to realize then is that .96-.2 has to be greater than .75 as stated. Because there is an infinite amount of numbers, or points on a number line, you must find length, or in this case, area. Create a graph, with an x-axis and y-axis. Now draw a square with side lengths 1. This area is equal to one, or 100 percent. By finding the area of numbers, or coordinates, that fit the condition, you can find the probability out of 100 percent that fits. Above, it says .96-.2 has to be greater than .75, so put into variables, that means y-x>.75 which simplifies to the inequality y>x+.75. Graph this as if it were y=x+.75 (or put it into a graphing calculator if you don't know how to do so). Now isolate the triangle that is formed by the line you drew and the square drawn earlier. this is an isosceles triangle, because the line has an elevation of 45 degrees. the side lengths are the same, and because there is .25 between .75 and 1, then both leg lengths of this triangle are .25. Now find the area of this triangle, and that is your answer
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∙ 13y ago
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