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A bag contains 4 white and 3 red balls. Two draws of one ball each are made without replacement. The probability that both the balls are red is?
By BYJU'S Exam Prep
Updated on: September 25th, 2023
The probability that both the balls are red is when a bag contains 4 white and 3 red balls and two draws of one ball each is made without replacement is 1/7. It is important to understand the there are two cases, one in which all the balls are there in the bag and the other in which all but one ball is present in the bag. The probability can be calculated by taking both these criteria into consideration.
Table of content
Probability of Drawing 2 Red Balls
Probability is the possibility of an event happening. It does not define whether an event will take place or not. Probability gives us the chances of the likelihood of it happening. To calculate the probability of drawing 2 red balls without replacement when a bag contains 4 white balls and 3 red balls can be calculated by the following means.
Solution
The first is to take the data provided to us into consideration and organize it into the following equations:
Number of white balls = 4
Number of red balls = 3
In the first round, the total number of balls in the bag will be:
Total number of balls in first round = 3+4 =7
After this, there was no replacement, it means that the ball was not replaced So,
Total number of balls in second round =7-1 = 6
Now, we will calculate the probability of both the balls drawn being red. Since we have total 3 balls, we will calculate it in the following manner:
=(3C1/7C1) x (2C1/6C1)
=3/7 x 2/6
= 1/7
Hence, the possibility of drawing 2 red balls without replacement from a bag with 4 white and 3 red balls is 1/7.
Summary:
A bag contains 4 white and 3 red balls. Two draws of one ball each are made without replacement. The probability that both the balls are red is?
If a bag contains 4 white and 3 red balls out of which two are drawn without replacement, the probability that both balls are red is 1/7. Probability is always in the range of 0 and 1 with 0 being an event being unlikely to happen and 1 being an event likely to happen.
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