  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 graduate2. only one will graduate3. 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 $${^{3}C_1}$$ wayshis 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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