Final Answer: The probability is approximately .
Steps
Step 1 :We are given that is a random variable with the binomial distribution with and . We are asked to calculate .
Step 2 :The binomial distribution is given by the formula: where: is the number of trials, is the number of successful trials, is the probability of success on each trial, and is the binomial coefficient, which can be calculated as .
Step 3 :In this case, we have , , and . We can substitute these values into the formula to find .
Step 4 :First, we calculate the binomial coefficient , which is .
Step 5 :Next, we substitute , , , and into the formula to get .
Step 6 :Final Answer: The probability is approximately .