prob = C(8,5)/C(15,5) = 56/3003 = 8/429
or
prob = (8/15)(7/14)(6/13)(5/12)(4/11)
= 8/429
or
prob = (8/15)(7/14)(6/13)(5/12)(4/11)
= 8/429
Step 1: Calculate the probability of drawing a black ball on the first draw.
There are a total of 7 pink and 8 black balls, so the probability of drawing a black ball on the first draw is 8/15.
Step 2: Since the balls are replaced after each draw, the probability of drawing a black ball on the second draw is also 8/15.
Step 3: Similarly, the probability of drawing a black ball on the third, fourth, and fifth draws is 8/15.
Step 4: Calculate the product of these probabilities.
Since the events are independent, we can multiply the probabilities. Therefore, the probability of drawing five black balls in succession is (8/15) * (8/15) * (8/15) * (8/15) * (8/15).
Step 5: Simplify the product.
Calculating this product gives us (8/15)^5.
Step 6: Calculate the final probability.
Evaluating (8/15)^5 gives us approximately 0.068.
Therefore, the probability that all five balls drawn from the urn are black is approximately 0.068, or 6.8%.
The total number of balls in the urn is 7 pink + 8 black = 15 balls. Since the balls are drawn with replacement, the probability of drawing a black ball on each draw will remain constant.
The probability of drawing a black ball on any given draw is calculated by dividing the number of black balls by the total number of balls in the urn.
Therefore, the probability of drawing a black ball on each draw is 8 black balls / 15 total balls = 8/15.
Since the balls are drawn with replacement, the probability of each draw is independent of the others. Therefore, to find the probability of all five balls being black, we need to multiply the probabilities of each individual draw.
So, the probability of drawing five black balls in succession is (8/15) * (8/15) * (8/15) * (8/15) * (8/15) = (8/15)^5 = 0.0590 (rounded to four decimal places).
Therefore, the probability that all five balls drawn from the urn are black is approximately 0.0590 or 5.90%.