Please help , I only need the second part of the question

Betty picks 4 random marbles from a bag containing 3 white , 4 yellow and 5 blue marbles
The probability that exactly 1 of the 4 marbles drawn is blue is (0.3535) .

The probability that at least 1 of the 4 marbles drawn is white is (0.2181) (0.2546) (0.5090) (0.7455) . Please help! Thank you :)

#1.

I agree with your first answer of .3535

#2.
at least 1 of the 4 marbles drawn is white
---> what you don't want is all non-white.

prob(none are white) = (9/12)(8/11)(7/10)(6/9)
= 14/55
prob(at least one white) = 1 - 14/55
= 41/55
= .7455 correct to 4 decimals

I have no idea what those 4 decimals in brackets represent, one of them is my answer.

Well, if the probability that exactly 1 of the 4 marbles drawn is blue is 0.3535, it means that Betty is pretty good at randomly picking blue marbles! Maybe she has a career as a professional marble picker, who knows?

As for the probability that at least 1 of the 4 marbles drawn is white, you've given me a few options: 0.2181, 0.2546, 0.5090, and 0.7455. Choosing between these probabilities is quite a challenge, isn't it? It's like trying to decide between different flavors of ice cream... except in this case, the flavors are probabilities. Yum!

But don't worry, I have a solution for you. Why not try a random number generator to pick one of those probabilities? It's like letting fate decide for you. Just make sure you don't get too ...umm... shaken up by the randomness, like a maraca. Haha!

Good luck with your probability choices!

To find the probability that at least 1 of the 4 marbles drawn is white, we can use the complement rule. The complement rule states that the probability of an event not occurring is equal to 1 minus the probability of the event occurring.

In this case, the event we want to find is the probability that none of the 4 marbles drawn is white. Let's calculate it step-by-step:

1. Find the probability of drawing a non-white marble on the first draw:
There are a total of 12 marbles in the bag, of which 9 are non-white. Therefore, the probability of drawing a non-white marble on the first draw is 9/12.

2. Find the probability of drawing a non-white marble on the second draw:
After the first draw, there are now 11 marbles in the bag, of which 8 are non-white. Therefore, the probability of drawing a non-white marble on the second draw is 8/11.

3. Repeat this process for the third and fourth draws:
After each draw, update the number of non-white marbles in the bag and calculate the probability of drawing a non-white marble on the next draw.

4. Calculate the probability of none of the 4 marbles being white:
To find this probability, you multiply the probabilities from each draw. In this case, it is (9/12) × (8/11) × (7/10) × (6/9).

5. Calculate the probability of at least 1 of the 4 marbles being white:
Finally, use the complement rule. The probability of at least 1 of the 4 marbles being white is equal to 1 minus the probability of none of the 4 marbles being white.

So, the probability that at least 1 of the 4 marbles drawn is white is 1 - [(9/12) × (8/11) × (7/10) × (6/9)].

To find the probability that at least one of the four marbles drawn is white, we need to calculate the complement of the event that none of the marbles drawn is white.

First, we find the probability of not drawing a white marble in one draw. Since there are a total of 12 marbles and 3 of them are white, the probability of not drawing a white marble is (12-3)/12 = 9/12 = 3/4.

Since the four draws are independent events, we can multiply the probabilities together to find the probability of not drawing a white marble in all four draws: (3/4)^4 = 81/256.

Now, to find the probability that at least one of the four marbles is white, we subtract the probability of not drawing a white marble from 1:

1 - 81/256 = 175/256 ≈ 0.6836

Therefore, the probability that at least one of the four marbles drawn is white is approximately 0.6836.

Hope this helps!