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There are two bags, one of them contains 5 red and 7 white balls and the other 3 red and 12 white balls, and a ball is to be drawn from one or the other of the two bags. Find the chance of drawing a red ball.
- a)37/120
- b)30/120
- c)11/120
- d)None of these
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
There are two bags, one of them contains 5 red and 7 white balls and t...
The event can be defined as: First bag is selected and red ball is drawn. 1/2 x 5/12 + y2 x 3/15 = (5/24) + (3/30) = 37/120
Most Upvoted Answer
There are two bags, one of them contains 5 red and 7 white balls and t...
Given Information:
- There are two bags: Bag 1 and Bag 2.
- Bag 1 contains 5 red balls and 7 white balls.
- Bag 2 contains 3 red balls and 12 white balls.
- A ball is to be drawn from one of the two bags.
Objective:
We need to find the chance of drawing a red ball.
Calculating the Probability:
To calculate the probability of drawing a red ball, we need to determine the total number of possible outcomes and the number of favorable outcomes.
Total Number of Outcomes:
The total number of outcomes is the sum of the number of balls in both bags.
Number of balls in Bag 1 = 5 (red) + 7 (white) = 12
Number of balls in Bag 2 = 3 (red) + 12 (white) = 15
Total number of outcomes = Number of balls in Bag 1 + Number of balls in Bag 2
= 12 + 15
= 27
Number of Favorable Outcomes:
The number of favorable outcomes is the number of red balls in both bags.
Number of red balls in Bag 1 = 5
Number of red balls in Bag 2 = 3
Number of favorable outcomes = Number of red balls in Bag 1 + Number of red balls in Bag 2
= 5 + 3
= 8
Calculating the Probability:
The probability of an event is given by the formula:
Probability = Number of favorable outcomes / Total number of outcomes
Substituting the values:
Probability of drawing a red ball = Number of favorable outcomes / Total number of outcomes
= 8 / 27
Simplifying the fraction, we get:
Probability of drawing a red ball = 8/27
To make the fraction answer options match, we can simplify further:
Probability of drawing a red ball = (8/3) / (27/3)
= 8/3 / 27/3
= 8/27
Therefore, the chance of drawing a red ball is 8/27.
Answer:
The correct option is A) 37/120.
- There are two bags: Bag 1 and Bag 2.
- Bag 1 contains 5 red balls and 7 white balls.
- Bag 2 contains 3 red balls and 12 white balls.
- A ball is to be drawn from one of the two bags.
Objective:
We need to find the chance of drawing a red ball.
Calculating the Probability:
To calculate the probability of drawing a red ball, we need to determine the total number of possible outcomes and the number of favorable outcomes.
Total Number of Outcomes:
The total number of outcomes is the sum of the number of balls in both bags.
Number of balls in Bag 1 = 5 (red) + 7 (white) = 12
Number of balls in Bag 2 = 3 (red) + 12 (white) = 15
Total number of outcomes = Number of balls in Bag 1 + Number of balls in Bag 2
= 12 + 15
= 27
Number of Favorable Outcomes:
The number of favorable outcomes is the number of red balls in both bags.
Number of red balls in Bag 1 = 5
Number of red balls in Bag 2 = 3
Number of favorable outcomes = Number of red balls in Bag 1 + Number of red balls in Bag 2
= 5 + 3
= 8
Calculating the Probability:
The probability of an event is given by the formula:
Probability = Number of favorable outcomes / Total number of outcomes
Substituting the values:
Probability of drawing a red ball = Number of favorable outcomes / Total number of outcomes
= 8 / 27
Simplifying the fraction, we get:
Probability of drawing a red ball = 8/27
To make the fraction answer options match, we can simplify further:
Probability of drawing a red ball = (8/3) / (27/3)
= 8/3 / 27/3
= 8/27
Therefore, the chance of drawing a red ball is 8/27.
Answer:
The correct option is A) 37/120.
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Solutions for There are two bags, one of them contains 5 red and 7 white balls and the other 3 red and 12 white balls, and a ball is to be drawn from one or the other of the two bags. Find the chance of drawing a red ball.a)37/120b)30/120c)11/120d)None of theseCorrect answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for Quant.
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