Question
A box contains 7 blue balls and 3 red balls. Two balls were picked at random at a time with replacement, compute the probability that both were of the different color
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Answer to a math question A box contains 7 blue balls and 3 red balls. Two balls were picked at random at a time with replacement, compute the probability that both were of the different color
Timmothy
4.899 Answers
To compute the probability that both balls picked are of different colors, we can calculate the probability of picking a blue ball first and a red ball second, and then add it to the probability of picking a red ball first and a blue ball second.
Step 1: Calculate the probability of picking a blue ball first and a red ball second.
The probability of picking a blue ball first is\frac{7}{10} \frac{3}{10}
Therefore, the probability of picking a blue ball first and a red ball second is\frac{7}{10} \cdot \frac{3}{10}
Step 2: Calculate the probability of picking a red ball first and a blue ball second.
The probability of picking a red ball first is\frac{3}{10} \frac{7}{10}
Therefore, the probability of picking a red ball first and a blue ball second is\frac{3}{10} \cdot \frac{7}{10}
Step 3: Add the probabilities from Step 1 and Step 2 to get the final answer.
The probability that both balls picked are of different colors is:
\frac{7}{10} \cdot \frac{3}{10} + \frac{3}{10} \cdot \frac{7}{10} = \frac{21}{100} + \frac{21}{100} = \frac{42}{100} = \frac{21}{50}
Answer: The probability that both balls picked are of different colors is\frac{21}{50}
Step 1: Calculate the probability of picking a blue ball first and a red ball second.
The probability of picking a blue ball first is
Therefore, the probability of picking a blue ball first and a red ball second is
Step 2: Calculate the probability of picking a red ball first and a blue ball second.
The probability of picking a red ball first is
Therefore, the probability of picking a red ball first and a blue ball second is
Step 3: Add the probabilities from Step 1 and Step 2 to get the final answer.
The probability that both balls picked are of different colors is:
Answer: The probability that both balls picked are of different colors is
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