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

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} . Since we replace the ball after the first pick, the probability of picking a red ball second is also \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} . Since we replace the ball after the first pick, the probability of picking a blue ball second is also \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}