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At a university 60% of the students are male and 40% are female. If ten students are selected at random,

  1. What is the probability that we have exactly seven females?
    I tried $0.4^7\cdot0.6\cdot3 = 0.00294912$ for this.
  2. What is the probability of selecting at least seven females?

I tried adding the sums of the probability of 7, 8, 9, and 10 females in the group. 0.003447194

Both of my answers were counted wrong. I was told that this is the correct way to solve this. Any help?

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  • $\begingroup$ Please add the self-study tag and modify your question to take into account the information here $\endgroup$
    – Glen_b
    Commented Mar 31, 2014 at 6:59
  • $\begingroup$ Thanks for adding the tag, but you still need to show us what you've tried and explain where your difficulties are. $\endgroup$
    – Glen_b
    Commented Mar 31, 2014 at 7:36
  • $\begingroup$ Consider: what events (situations) are included in "At least seven females"? $\endgroup$
    – Glen_b
    Commented Mar 31, 2014 at 7:38
  • $\begingroup$ Your idea (of adding the probability of 7, 8, 9 and 10 females) is correct. $\endgroup$
    – Glen_b
    Commented Mar 31, 2014 at 8:37

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In (1) you haven't accounted for all the different ways that you can get 7 females and 3 males.

In (2) your idea was correct (of adding the probability of 7, 8, 9 and 10 females), but if you have the probability in (1) wrong, you'll have the same mistake.

(You might want to read about the binomial distribution.)

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