While shifting glass bottles from one country to the other, on an average, 1 out of 9 bottles breaks. What is the probability that out of 4 bottles, at least 3 will arrive safely?
Solution
Probability of at least 3 bottles being safe = Probability of at least 3 bottles being safe + Probability of all 4 bottles being safe
To find Probability of all 4 bottles being safe, we also need to multiply the result with 4, since any of the four bottles can be damaged.
Also, probability of a bottle being damaged is $$\ \frac{\ 9}{10}$$
Hence, Probability of at least 3 bottles being safe = $$\ \ \left(\frac{\ 8}{9}\right)^4$$ + 4$$\ \times\ $$ $$\ \left(\frac{\ 8}{9}\right)^3\times\ \left(\ \frac{\ 1}{9}\right)$$
On solving this, we get the answer as $$\frac{\ 2048}{2187}$$
