SOLUTION: Hospital records show that 20% of the cases of a certain disease are fatal. Find the probability that out of 5 patients admitted with this disease a. all will recover b. exactly

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Question 1157344: Hospital records show that 20% of the cases of a certain disease are fatal. Find the probability that out of 5 patients admitted with this disease
a. all will recover
b. exactly 2 will recover
c. at least 2 will recover
Answer by VFBundy(438) About Me  (Show Source):
You can put this solution on YOUR website!
a. all will recover

%280.8%29%5E5 = 0.32768

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b. exactly 2 will recover

%280.8%29%5E2+%2A+%280.2%29%5E3+%2A+%285%21%2F%282%21%2A3%21%29%29 = %280.8%29%5E2+%2A+%280.2%29%5E3+%2A+10 = 0.64 * 0.008 * 10 = 0.0512

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c. at least 2 will recover

Find the probability that exactly one will recover AND the probability that none will recover. Add these together and subtract that result from 1.

Probability exactly one will recover:

%280.8%29%5E1+%2A+%280.2%29%5E4+%2A+%285%21%2F%281%21%2A4%21%29%29 = %280.8%29%5E1+%2A+%280.2%29%5E4+%2A+5 = 0.8 * 0.0016 * 5 = 0.0064

Probability none will recover:

%280.2%29%5E5 = 0.00032

Probability exactly one will recover PLUS probability none will recover:

0.0064 + 0.00032 = 0.00672

Probability at least two will recover:

1 - 0.00672 = 0.99328