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In a bag that contains white, black, and red balls only, a ball is drawn at random from the bag. If the probability of getting a white ball is 3/10 and that of a black ball is 2/5, then find the probability of getting a red ball. If the bag contains 20 black balls, then find the total number of balls in the bag.

Options:
a. 1​/5
b. 1/4​
c. 1/3​
d. 1/2​

User Rvirding
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1 Answer

6 votes

Final answer:

To find the probability of getting a red ball, subtract the sum of the probabilities of getting a white and black ball from 1. The probability of getting a red ball is 1/2. If the bag contains 20 black balls, the total number of balls in the bag is 50. The correct answer is d. 1/2​.

Step-by-step explanation:

To find the probability of getting a red ball, you can subtract the sum of the probabilities of getting a white ball and a black ball from 1. Since the probability of getting a white ball is 3/10 and the probability of getting a black ball is 2/5, the probability of getting a red ball is 1 - (3/10 + 2/5) = 1/2.

If the bag contains 20 black balls, then we can find the total number of balls in the bag using the equation:

Probability of a white ball + Probability of a black ball + Probability of a red ball = 1
3/10 + 2/5 + Probability of a red ball = 1
Probability of a red ball = 1 - (3/10 + 2/5)
Probability of a red ball = 1/2

Let's represent the total number of balls in the bag as x. Since the probability of a black ball is 2/5 and there are 20 black balls, we can set up the proportion:

2/5 = 20/x

Cross-multiplying, we get:

2x = 5 * 20

2x = 100

x = 50

Therefore, the total number of balls in the bag is 50.

User Nunoarruda
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