Determine the probability that X is less than 3: $P(X<3), n=7, p=0.6$

Step 1 ：We are given a random variable X that follows a binomial distribution with parameters n=7 and p=0.6. We are asked to find the probability that X is less than 3.

Step 2 ：This means we need to find the sum of the probabilities of X being 0, 1, or 2.

Step 3 ：The formula for the probability mass function of a binomial distribution is: \(P(X=k) = C(n, k) * p^k * (1-p)^(n-k)\), where C(n, k) is the binomial coefficient, which can be calculated as \(n! / (k!(n-k)!)\), and ! denotes factorial.

Step 4 ：Substituting the given values into the formula, we get the probability as approximately 0.09625600000000004.

Step 5 ：Final Answer: The probability that X is less than 3 is approximately \(\boxed{0.096}\).