answer:
To find the probability of randomly pulling 5 red balls out of 7 from a bag containing 11 balls (7 red and 4 black), we can use the concept of combinations and the formula for probability.
Step 1: Determine the total number of possible outcomes. In this case, the total number of possible outcomes is the number of ways we can choose 7 balls from the 11 balls in the bag. We can calculate this using the combination formula: nCr = n! / (r!(n-r)!), where n is the total number of items and r is the number of items we want to choose. In this case, we have 11 balls and we want to choose 7, so the total number of possible outcomes is 11C7 = 11! / (7!(11-7)!) = 330.
Step 2: Determine the number of favorable outcomes. The favorable outcomes are the number of ways we can choose 5 red balls from the 7 red balls in the bag. We can calculate this using the combination formula: nCr = n! / (r!(n-r)!), where n is the total number of items and r is the number of items we want to choose. In this case, we have 7 red balls and we want to choose 5, so the number of favorable outcomes is 7C5 = 7! / (5!(7-5)!) = 21.
Step 3: Calculate the probability. The probability of randomly pulling 5 red balls out of 7 from the bag is the number of favorable outcomes divided by the total number of possible outcomes: 21 / 330 = 0.0636 (rounded to four decimal places).
Therefore, the probability that if you randomly pull 7 balls from the bag, 5 will be red is approximately 0.0636, or 6.36%.
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