There are 52 balls in a box. 13 are red, 20 are white, and the other are blue. You pick up 5 balls without replacement. What is the probability that you pick up at least 1 red balls?

Question

BlackTom AI · Accepted Answer

To tackle this problem, I’ll use the complement rule: it’s often easier to find the probability of the opposite event and subtract from 1.
First, identify how many non-red balls there are. There are 52 total balls, with 13 red, so there are 39 non-red balls (20 white and 19 blue).
We draw 5 balls without replacement, and we want the probability of getting at least one red. So we compute the probability of getting zero red balls and subtract from 1.
The number of ways to choose 5 balls all from the non-red group is C(39,5). The total number of ways to choose any 5 balls from the box is C(52,5).
Thus, P(no red) = C(39,5) / C(52,5). Compute these values: C(52,5) = 2,598,960 and C(39,5) = 575,757. So P(no red) = 575,757 / 2,598,960 ≈ 0.2217.
Therefore, P(at least one red) = 1 − P(no red) ≈ 1 − 0.2217 ≈ 0.7783, which rounds to 0.78.
Now evaluate the given options:
Option 1: 0.78 — This matches the computed probability after rounding, so it is correct.
Option 2: 0.41 — This is significantly smaller than the computed probability and would imply a much lower chance of drawing a red ball; it does not fit the calculation.
Option 3: None of the other three — This would be true only if none of the provided options were correct; since 0.78 is correct, this option is false.
Option 4: 0.22 — This is approximately the probability of drawing zero red balls, i.e., P(no red), not P(at least one red); it represents the complement, not the desired probability.
In summary, the reasoning shows that the correct probability is about 0.778, which is represented by 0.78 among the choices.

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There are 52 balls in a box. 13 are red, 20 are white, and the other are blue. You pick up 5 balls without replacement. What is the probability that you pick up at least 1 red balls?

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MGS*2150*W07 final- Requires Respondus LockDown Browser

There are 52 balls in a box. 13 are red, 20 are white, and the other are blue. You pick up 5 balls without replacement. What is the probability that you pick up at least 1 red balls?

View Explanation

Log in for full answers

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