Final answer:
The probability of drawing no black balls is 5/12, and the probability of drawing only one black ball is 7/3960.
Adding these probabilities gives us the overall probability of 199/440 or approximately 0.4523.
Step-by-step explanation:
To find the probability that no more than one black ball is drawn, we need to consider two cases: drawing no black balls and drawing only one black ball.
Case 1: Drawing no black balls
The probability of drawing no black balls is the same as drawing all red balls.
There are 5 red balls out of a total of 12 balls in the urn, so the probability is 5/12.
Case 2: Drawing only one black ball
The probability of drawing one black ball is the product of the probability of drawing one black ball and the probability of drawing four red balls.
The probability of drawing one black ball is 7/12 and the probability of drawing four red balls is:
4/11 * 3/10 * 2/9 * 1/8
= 1/330.
Therefore, the probability of drawing only one black ball is :
7/12 * 1/330
= 7/3960.
Finally, we add the probabilities from both cases to get the probability that no more than one black ball is drawn:
5/12 + 7/3960
= 199/440 or approximately 0.4523 when rounded to four decimal places.