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Question Number 168035 by pete last updated on 01/Apr/22

In an examination, the probability of charles  scoring the highest mark in Maths, Physics  and Chemistry are 0.90, 0.75 and 0.80 respectively.  Calculate the probability that he will get  the highest mark in at least 3 subjects.

$$\mathrm{In}\:\mathrm{an}\:\mathrm{examination},\:\mathrm{the}\:\mathrm{probability}\:\mathrm{of}\:\mathrm{charles} \\ $$$$\mathrm{scoring}\:\mathrm{the}\:\mathrm{highest}\:\mathrm{mark}\:\mathrm{in}\:\mathrm{Maths},\:\mathrm{Physics} \\ $$$$\mathrm{and}\:\mathrm{Chemistry}\:\mathrm{are}\:\mathrm{0}.\mathrm{90},\:\mathrm{0}.\mathrm{75}\:\mathrm{and}\:\mathrm{0}.\mathrm{80}\:\mathrm{respectively}. \\ $$$$\mathrm{Calculate}\:\mathrm{the}\:\mathrm{probability}\:\mathrm{that}\:\mathrm{he}\:\mathrm{will}\:\mathrm{get} \\ $$$$\mathrm{the}\:\mathrm{highest}\:\mathrm{mark}\:\mathrm{in}\:\mathrm{at}\:\mathrm{least}\:\mathrm{3}\:\mathrm{subjects}. \\ $$

Commented by MJS_new last updated on 01/Apr/22

“at least 3 subjects” with 3 subjects given  means “in all 3 subjects” ⇒  .9×.75×.8=.54

$$``\mathrm{at}\:\mathrm{least}\:\mathrm{3}\:\mathrm{subjects}''\:\mathrm{with}\:\mathrm{3}\:\mathrm{subjects}\:\mathrm{given} \\ $$$$\mathrm{means}\:``\mathrm{in}\:\mathrm{all}\:\mathrm{3}\:\mathrm{subjects}''\:\Rightarrow \\ $$$$.\mathrm{9}×.\mathrm{75}×.\mathrm{8}=.\mathrm{54} \\ $$

Commented by pete last updated on 02/Apr/22

Thanks Sir

$$\mathrm{Thanks}\:\mathrm{Sir} \\ $$

Commented by pete last updated on 05/Apr/22

thanks very much

$$\mathrm{thanks}\:\mathrm{very}\:\mathrm{much} \\ $$

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