Why are we adding X in this Bernoulli distribution question?

Question

An interviewer is given a list of people she can interview. If the interviewer needs to interview 6 people, and if each person (independently) agrees to be interviewed with probability 3/4, what is the probability that her list of people will enable her to obtain her necessary number of interviews if the list consists of (a) 6 people and (b) 10 people? For part (b), what is the probability that the interviewer will speak to exactly (c) 7 people and (d) 9 people on the list?

For part (b), I thought I would use the Bernoulli Distribution and find out the value when X = 6 (since she wants 6 successes).

I would have P(X=6) and get some answer. However the answer is P(X>=6) = P(X=6) + P(X=7) + P(X=8) + P(X=9) + P(X=10)

Why are they getting the sum for all bigger than 6 and not just 6?

EDIT: for part c) I think I'm supposed to use a negative binomial but I'm stuck after that.

Answer 1

The interviewer doesn't want 6 successes, she wants at least 6 successes. The key is:

her to obtain her necessary number of interviews

If she has 7 interviews, that's fine. If she has 8 that's fine too, etc.

Answer 2

In the Bernoulli distribution: X~Bernoulli(10,3/4), P(X=6) gives the probability that EXACTLY 6 people accept to be interviewed. Since you want the probability of her obtaining at least 6 people, the answer is:

P(X>=6) = P(X=6) + P(X=7) + P(X=8) + P(X=9) + P(X=10), as stated.