There are 14 black, 16 white, and 10 red balls in a box. What is the probability of selecting 1 black ball, then 1 red ball, and then 1 white ball, replacing the ball each time?

Rationale

The probability of selecting 1 black ball, then 1 red ball, and then 1 white ball, with replacement, is 7/200.

To find this probability, we calculate the probability of each selection sequentially while considering that the total number of balls remains constant due to replacement. The probability of each event is multiplied together to determine the overall probability.

A (7/200) CORRECT

This is the correct answer. The probability of selecting a black ball is 14/40, a red ball is 10/40, and a white ball is 16/40. Multiplying these probabilities gives (14/40) * (10/40) * (16/40) = 2240/64000, which simplifies to 7/200.

B (7/100) YOUR ANSWER

This option incorrectly assumes a higher probability than what is calculated. The total probability must account for the replacement of balls, which keeps the denominator at 40 for each selection. The correct multiplication of the probabilities yields a smaller fraction, which does not support this choice.

C (21/200) YOUR ANSWER

This choice miscalculates the combined probability of choosing the balls sequentially. The multiplication of the individual probabilities does not yield this result; instead, it results in a smaller fraction that is accurately represented by option A.

D (Jul-50) YOUR ANSWER

This option is invalid as it does not represent a proper fraction or decimal. It appears to be a typographical error or misinterpretation of a numerical value, failing to adhere to the expected format for expressing probabilities.

Conclusion

The accurate calculation of the probability of selecting 1 black ball, followed by 1 red ball, and then 1 white ball, with replacement, is reflected in the answer 7/200. Each step of the probability calculation confirms that the total number of balls remains constant, which is crucial for determining the correct overall probability. Other options either miscalculate or fail to represent valid probabilities, reinforcing the correctness of option A.

There are 14 black, 16 white, and 10 red balls in a box. What is the probability of selecting 1 black ball, then 1 red ball, and then 1 white ball, replacing the ball each time?

The probability of selecting 1 black ball, then 1 red ball, and then 1 white ball, with replacement, is 7/200.

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