There are 8 red, 5 yellow, and 7 green cubes in a box. What is the probability of drawing a yellow cube and then a green cube if the first cube is not replaced before the second cube is drawn?

i think thats a 1 in 20th chance

Answered by Anonymous | 2024-06-12

The probability of drawing a yellow cube followed by a green cube without replacement from a box with 8 red, 5 yellow, and 7 green cubes is 7/76.
The student has asked about the probability of drawing two colored cubes in sequence without replacement from a box containing a specific number of red, yellow, and green cubes. To find this probability, we must consider the probability of both events happening one after the other. The probability of drawing a yellow cube first is 5 divided by the total number of cubes, which is 20 (8 red + 5 yellow + 7 green). If a yellow cube is drawn first, it is not replaced, so there is now one less cube in the box making the total count 19.
The probability of drawing a green cube after having drawn a yellow cube is 7 out of these 19 remaining cubes. Hence, the combined probability of both events is the product of the probabilities of each event: For the first draw, it's 5/20, and for the second draw, it's 7/19. Therefore, the probability of drawing a yellow cube followed by a green cube is (5/20) multiplied by (7/19), which equals 35/380 or 7/76 when simplified.

Answered by DonalSutherland | 2024-06-24

The probability of drawing a yellow cube followed by a green cube without replacement from a box of cubes is 76 7 ​ . This calculation is derived from the individual probabilities of drawing each cube based on the number of total cubes available. To find the result, you multiply the probabilities of each draw together.
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Answered by DonalSutherland | 2024-12-24