Question

In a game, 80 marbles numbered 00 through 79 are placed in a box. A player draws 1 marble at random from the box. Without replacing the first marble, the player draws a second marble at random. If both marbles drawn have the same ones digit, the player is a winner. If the first marble drawn is numbered 35, what is the probability that the player will be a winner on the next draw?

a) 1/1
b) 1/9
c) 1/8
d) 1/7
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Answer 1

After drawing the first marble numbered 35, with no replacement, the probability of drawing another marble with the same ones digit from the remaining 79 marbles is 7/79. This simplifies to a probability slightly less than 1/11, which is not one of the exact answer choices provided.

Step-by-step explanation:

In a game where 80 marbles numbered 00 through 79 are in a box, if the first marble drawn is numbered 35, to win, the player needs to draw a second marble with the same ones digit, in this case, a '5'. Since the numbers end in 0-9, there are initially 8 marbles with the same ones digit (05, 15, 25, 35, 45, 55, 65, 75). But since the 35 marble has already been drawn, that leaves 7 marbles that can result in a win (05, 15, 25, 45, 55, 65, 75).

However, there are now only 79 marbles left in the box since the first marble is not replaced. Therefore, the probability that the player will draw another marble ending in '5' is 7 chances out of 79.

The closest answer choice that simplifies this fraction is 1/11, even though it is not exactly correct. The actual fraction does not perfectly simplify, but when converted to a decimal or a percentage, it would show a probability slightly less than 1/11.