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Question

The probability that a student entering a university will graduate is $$0.4$$. Find the following probabilities out of $$3$$ students of the university:
1. none will graduate
2. only one will graduate
3. all will graduate.


Solution

Probability that $$\alpha$$ student graduates$$=0.4$$

(i) Probability that none of $$3$$ students graduate$$=(1-0.4)\times (1-0.4)\times (1-0.4)$$

Probability that student $$(1)$$ doesn't graduate
$$\Rightarrow 0.6\times 0.6\times 0.6$$
$$\Rightarrow 0.216$$
$$\therefore$$ Probability that none of $$3$$ students graduate$$=0.216$$

(ii) The only one will graduate.
we select one of $$3$$ in $${^{3}C_1}$$ ways
his probability of passing $$=0.4$$
remaining two fail$$\Rightarrow 0.6\times 0.6$$

probability $$={^3C_1}\times (0.4)\times (0.6)\times (0.6)$$
$$=3\times 0.4\times 0.36$$
Probability that only one will graduate$$\Rightarrow 0.432$$

(iii) Probability that all students graduate$$=(0.4)(0.4) (0.4)$$
$$=0.064$$
$$\therefore$$ Probability that all will graduate$$=0.064$$.

Mathematics

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