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Probability of an event, P, occurring exactly r times is:
where n is the number of trials (5 in this case), p is the probability (.8), r the number desired (such as 3 students being alive), and q=1-p which is .2 in this case.
Often we solve such problems by adding a number of probabilities. For example, if it's the probability that "at least" 2 survive, we add the probability for 2, 3, 4 and 5 found with the above formula.
1. P(exactly 3 alive) gives r =3. So P = 
= 20.48%
2. P(at least 3 alive) means 
so add the P(3) + P(4) + P(5).
P(3)= 20.48%
P(4)= 
= 40.96%
P(5) = 
= 32.77%
P(3 or more) = P(3)+P(4)+P(5)=20.48+40.96+32.77 = 94.21%
3. P(at most 2) means 
so add P(2) + P(1) + P(0).
P(2)= 
= 5.12%
P(1) = 
= .64%
P(0) = 
= .032%
P(at most 2) = P(2)+P(1)+P(0)= 5.12% + .64% +.032% = 5.79%
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