wooden balls are numbered 1-75. Five balls are drawn at random. What is the probability of drawing 5 consecutive numbers if no replacement occurs.?

The first ball has a 1/75 chance of being selected. The second ball can be from either above or below the first, so it has a 2/74 chance of being chosen. The same process of selection continues through the fifth ball.

To find the probability that all of these events will occur, you need to multiply the probability of the individual events.

With this information, you should be able to answer your own question.

I hope this helps. Thanks for asking.

I don't think that's right PsyDAG. What if the first ball is #1 -- there is no number below. Second, what if you picked balls in the following order; 5,3,1,2,4 would this be counted as a "success" as the numbers are, when rearranged, consecutive.

I think this is a combinatorial problem. The number of ways do draw 5 balls from a bag of 75 is 75-choose-5 or (75!)/((75-5)!*(5!)) where ! denotes factorial. This translates to (75*74*73*72*71)/(1*2*3*4*5) = 17259390. Now then, there are exactly 70 5-consecutive-balls combinations that could be drawn. (1,2,3,4,5), (2,3,4,5,6), ... (71,72,73,74,75). So, the probability is 70/17259390 = something very small

I apologize for the incorrect response. You are right, the previous explanation was not accurate. Thank you for pointing that out.

You are correct in approaching this problem as a combinatorial problem. The number of ways to draw 5 balls from a bag of 75 is given by the formula 75-choose-5 or (75!)/((75-5)!*(5!)), where "!" denotes factorial. This calculation gives us the total number of possible outcomes.

In this case, there are exactly 70 combinations of consecutive 5-ball sets that can be drawn. These sets include (1,2,3,4,5), (2,3,4,5,6), and so on up to (71,72,73,74,75).

To calculate the probability of drawing 5 consecutive numbers, we divide the number of successful outcomes (70) by the total number of possible outcomes (17,259,390). Therefore, the probability is 70/17,259,390, which is indeed a very small value.

I apologize for the confusion caused by the earlier response. Thank you for bringing this to my attention.