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Question Number 132551 by liberty last updated on 15/Feb/21

A conservative design team , call it C  and innovative design team call  it N , are asked to separately design  a new product within a month.  From past experience we know that  (a) The probability that team C is successful is 2/3  (b) The probability that team N is successful 1/2  (c) The probability that at least one  team is successful is 3/4  Assuming that exactly one successful  design is produced, what is the  probability that it was designed by  team N ?

$$\mathrm{A}\:\mathrm{conservative}\:\mathrm{design}\:\mathrm{team}\:,\:\mathrm{call}\:\mathrm{it}\:\mathrm{C} \\ $$$$\mathrm{and}\:\mathrm{innovative}\:\mathrm{design}\:\mathrm{team}\:\mathrm{call} \\ $$$$\mathrm{it}\:\mathrm{N}\:,\:\mathrm{are}\:\mathrm{asked}\:\mathrm{to}\:\mathrm{separately}\:\mathrm{design} \\ $$$$\mathrm{a}\:\mathrm{new}\:\mathrm{product}\:\mathrm{within}\:\mathrm{a}\:\mathrm{month}. \\ $$$$\mathrm{From}\:\mathrm{past}\:\mathrm{experience}\:\mathrm{we}\:\mathrm{know}\:\mathrm{that} \\ $$$$\left(\mathrm{a}\right)\:\mathrm{The}\:\mathrm{probability}\:\mathrm{that}\:\mathrm{team}\:\mathrm{C}\:\mathrm{is}\:\mathrm{successful}\:\mathrm{is}\:\mathrm{2}/\mathrm{3} \\ $$$$\left(\mathrm{b}\right)\:\mathrm{The}\:\mathrm{probability}\:\mathrm{that}\:\mathrm{team}\:\mathrm{N}\:\mathrm{is}\:\mathrm{successful}\:\mathrm{1}/\mathrm{2} \\ $$$$\left(\mathrm{c}\right)\:\mathrm{The}\:\mathrm{probability}\:\mathrm{that}\:\mathrm{at}\:\mathrm{least}\:\mathrm{one} \\ $$$$\mathrm{team}\:\mathrm{is}\:\mathrm{successful}\:\mathrm{is}\:\mathrm{3}/\mathrm{4} \\ $$$$\mathrm{Assuming}\:\mathrm{that}\:\mathrm{exactly}\:\mathrm{one}\:\mathrm{successful} \\ $$$$\mathrm{design}\:\mathrm{is}\:\mathrm{produced},\:\mathrm{what}\:\mathrm{is}\:\mathrm{the} \\ $$$$\mathrm{probability}\:\mathrm{that}\:\mathrm{it}\:\mathrm{was}\:\mathrm{designed}\:\mathrm{by} \\ $$$$\mathrm{team}\:\mathrm{N}\:? \\ $$

Answered by guyyy last updated on 20/Feb/21

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