A bag has 32 yellow, red, blue and green balls. If one ball

I used to be so confused about probability. However, I tried my best to educate myself and got a really good result on my exams.
Here's how you do it. The sum of all the probability will always be 100% (i.e. 1). Probability also = favourable outcomes/possible outcomes. In this question, there are 32 blue, red, green and yellow balls. There are 2 ways to do this question:

1) the sum will always be 1 for the probability. Therefore, if green = 0.5, blue = 0.25, the sum of yellow and red will be 1-0.5-0.25 = 1/4. So the probability of you drawing red or yellow is 1/4.

2) green = 0.5. So the number of green balls are 0.5*32 = 16. blue = 0.25. So the number of blue balls are 0.25*32 = 8. The total red and yellow balls will then be 32-16-8=8. So, the probability will then be favourable outcomes/possible outcomes which is 8/32=1/4.

Hope I explained this clear enough because I know that probability is so hard to understand at the beginning. For more information, you can check out links in other website about probability.

[quote="rohan2345"]A bag has 32 yellow, red, blue and green balls. If one ball is drawn from the bag at random, the probability that it will be green is 0.5, and the probability that it will be blue is 0.25. What is the probability that the ball will be either red or yellow?

Total Balls: 32

There are Yellow, Red, Blue and Green balls, is the count of these balls given? Or is there any way we can determine the count? Yes

Probability of Green Balls: 0.5

P (Green) = No.of Greeg Balls/Total No. of Balls

0.5 = G/32

G = 16

Similarly, we can determine the Blue Balls = 8

Remaining: 32 - 16 - 8 = 8 Balls

We are asked to find the Probability for Either red or yellow = 1/8 + 1/8 = 2/8 = 1/4

Hence, Answer is B = 1/4

Not sure if this qualifies for a 600-700 level question

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Ans: B

The probability of an event can be defined as the the ratio,
of the favorable outcomes to the total outcomes.


Coming to the problem, when it is said probability that the ball is green is 0.5
Converted into a fraction, 0.5 is \(\frac{1}{2}\)
Since we are given there are 32 balls in total, denominator has to be 32.
\(\frac{1}{2}\) = \(\frac{16}{32}\)(which translates to a total of 16 green balls in the bag)

Similarly, the probability of ball being blue is 0.25, which is \(\frac{1}{4}\)
Using the same logic, there are a total of 8 blue balls in the bag.

In the question stem, it is clearly given that the balls can be one of 4 colors : Blue, Green, Red or Yellow.
Red + Yellow + Blue + Green = Total

Red + Yellow = Total - Blue - Green = 32 - 8 - 16 = 8
Probability of finding red or yellow ball in the bag is \(\frac{8}{32}\) = \(\frac{1}{4}\)(Option B)

Since the probability that a green marble is selected is 0.5 = 1/2:

g/32 = 1/2

2g = 32

g = 16

Since the probability that a blue marble is selected is 0.25 = 1/4:

b/32 = 1/4

4b = 32

b = 8

Since there are 16 + 8 = 24 green and blue marbles, there are 32 - 24 = 8 red and yellow marbles.

Thus, the probability of selecting either a red or yellow marble is 8/32 = 1/4.

Alternate solution:

Since P(yellow) + P(red) + P(blue) + P(green) = 1, P(blue) = 0.25 = ¼, and P(green) = 0.5 = ½, we can say:

P(yellow) + P(red) + ¼ + ½ = 1

P(yellow) + P(red) + ¾ = 1

P(yellow) + P(red) = ¼

Since the yellow balls and red balls are mutually exclusive, P(yellow) + P(red) = P(yellow or red), and thus P(yellow or red) = ¼.

Answer: B

y + r + g + b = T
(y + r)/T = ?
y + r = T - (g + b)
y + r = T - (T/2 + T/4)
y + r = T/4
(y + r)/T = 1/4

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