A bag contains 5 red balls and 4 white balls. Two balls are drawn at random from the bag. The first ball drawn is put back into the bag before the second ball is drawn. What is the probability that two balls drawn are both red?
0.277777777
To find the probability that two balls drawn are both red, we need to determine the total number of possible outcomes and the number of favorable outcomes.
Total number of possible outcomes:
When drawing the first ball, there are 9 balls in total (5 red + 4 white). After replacing the first ball, there are still 9 balls in the bag. Therefore, there are 9 possible outcomes for the first ball and 9 possible outcomes for the second ball. So, the total number of possible outcomes is 9 * 9 = 81.
Number of favorable outcomes:
The probability of drawing a red ball on the first draw is 5/9 (since there are 5 red balls out of 9 total balls). Since the first ball is put back into the bag, the probability of drawing a red ball on the second draw is also 5/9. The probability of both events happening is the product of their individual probabilities. So, the number of favorable outcomes is (5/9) * (5/9) = 25/81.
Probability:
The probability of two balls drawn being both red is the number of favorable outcomes divided by the total number of possible outcomes:
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = (25/81) / (81/81)
Probability = 25/81
Therefore, the probability that two balls drawn at random from the bag are both red is 25/81.