<p>2, 2.5, 3, 5.1, 5.5, 6
A number is to be chosen at random from the list above. The probability is 1/3 that the number chosen will be greater than x .
What is one possible value of x ?
Answer: 5.1 ≤ x < 5.5</p>
<p>But can anyone explain it?
Thank you! :)</p>
<p>There are 6 numbers. If it’s in the range that you’ve shown and you pick each of the 6 numbers, in 4 instances the number picked is not greater than x and in 2 instances (5.5 and 6) it is. So the probability is 2/6=1/3 that the number you pick is larger than x. </p>
<p>If x is below 5.1, in at least 3 instances (5.1, 5.5, 6), the number picked will be greater so the probability will be 1/2 or more; while if x>=5.5, you will have fewer than 2 out of 6 cases where the number is greater, ie., the probability will be 1/6 or less.</p>
<p>Thank you! :)</p>
<p>Dad of 3, I don’t get your explanation…</p>
<p>Power, look at the ways you can categorize x:
<p>2) the next grouping is x is 2 or more, but less than 2.5, ie., 2 <= x < 2.5
again, it doesn’t matter if it is 2.0 or 2.1 or 2.2 or whatever as long as it is in this range. When you draw the 6 numbers, in one instance (number 2), the number drawn wont be greater than x (at best it could be equal to x, but never greater). In the remaining 5 cases, the number drawn will be greater than x. So the probability is 5/6 that the number drawn is greater than x for this range.</p>
<p>keep doing this for all the seven ranges for x and see what the probability is in each case. The last case is x >=6, where whatever number you draw, it will not be higher than x, so the probability for that range will be 0.</p>
<p>Check out the site artofproblemsolving.com which has a lot of math discussions and problems.</p>
<p>Ah - I get it. Thank you!!</p>