Final answer:
The probability of drawing two red balls in succession from an urn containing 10 green, 4 red, and 1 white ball without replacement is calculated by multiplying the individual probabilities of each draw, resulting in a combined probability of 2/35.
Step-by-step explanation:
The student's question pertains to the subject of probability, specifically the probability of drawing balls of different colors from an urn without replacement.
When a ball is drawn, recorded, and not replaced, the total number of balls in the urn decreases, thus changing the probabilities for the subsequent draw. Let's look at the given scenario where there are 10 green, 4 red, and 1 white ball in the urn, making a total of 15 balls.
If you draw a red ball on the first draw, the probability of doing so is \(\frac{4}{15}\). Now since you're drawing without replacement, if the first ball drawn is red, there will only be 3 red and 14 total balls left.
So, the probability of drawing a second red ball would then be \(\frac{3}{14}\). To find the combined probability of drawing two red balls in succession without replacement, you would multiply these two probabilities: \(\frac{4}{15} \times \frac{3}{14} = \frac{12}{210} = \frac{2}{35}\).