# exactly, and at least : Probability

thanks for looking at my question. Any help would be appreciated!

at a university 60% of the students are male and 40% are female

If ten students are selected at random, what is the probability that we have exactly seven females?

and

What is the probability of selecting at least seven females?

a simple explanation would be greatly appreciated, i just cant seem to figure this one out. Thanks!

## 1 Answer

Hint: It is fairly simple to calculate what the probability of selecting exactly $i$ females for any value of $i$ is. Take a look at the binomial distribution.

• I have looked at the binomial distribution but I am confused by the explanation given in my textbook, that is why I am asking for help here. Mar 31, 2014 at 7:28
• Try and calculate the probability that exactly $7$ females will be selected. Then, the probabilitz that exactly $8$ will be selected and so on. Sum them all to get the probability of selecting at least $7$.
– 5xum
Mar 31, 2014 at 7:39
• so i did what you said and got 0.00294912 or (0.4)^7*(0.6)*3 for the first question and 0.003447194 for the second question by adding the sums of all the probability for 7 8 9 and 10 females, but the answer was still counted wrong. Do you have any insight on this by chance ? Mar 31, 2014 at 8:00
• You forgot the binomial coefficients. If an event has a chance of happening of $p$, then it will happen $k$ times in $n$ attempts with the probability ${n\choose k}p^k(1-p)^{n-k}$, not only $p^k(1-p)^{n-k}$.
– 5xum
Mar 31, 2014 at 9:49
• If you are having trouble with notation, $$\dbinom{n}{k} = {{_n}C_k}$$ Jul 19, 2019 at 13:03