$3.$ Answer the following questions on reliability

$3\mathrm{.}1.$ A product is made up of six components $\backslash ($ A$,$ B$,$ C$,$ D$,$ E $\backslash ),$ and $\backslash ($ F $\backslash ).$ They are wired in series with reliabilities of $\backslash (\mathrm{.}95,\mathrm{.}98,\mathrm{.}94,\mathrm{.}96,\mathrm{.}98\backslash ),$ and $\mathrm{.}97$ for components A through F$,$ respectively. What is the overall reliability for this product? $(7$ Points$)$

$3\mathrm{.}2.$ Suppose backup components are introduced for components $\backslash ($ A $\backslash )$ and $\backslash ($ C $\backslash ).$ These components have identical reliabilities to $\backslash ($ A $\backslash )$ and $\backslash ($ C $\backslash ).$ What is now the overall reliability for the product? $(7$ Points$)$

$3\mathrm{.}3.$ Suppose that redundant components are introduced for all of the components in Problem $3\mathrm{.}1.$ What is now the overall reliability for the product? $(7$ Points$)$

$3\mathrm{.}4.$ A radio is made up of $125$ components. What would have to be the average reliability for each component for the radio to have a reliability of $\backslash (98\backslash \%\backslash )$ over its useful life? $(7$ Points$)$

$3\mathrm{.}5.$ The Collier Company tested $200$ products for $100$ hours each. In this time, they experienced $12$ breakdowns. Compute the number of failures per hour. What is the mean time between failures? $(7$ Points$)$

$3\mathrm{.}6.$ Suppose a product is designed to function for $10,000$ hours with a $\backslash (3\backslash \%\backslash )$ chance of failure. Find the average number of failures per hour $\backslash ((\backslash$lambda$)\backslash )$ and the MTTF$.(7$ Points$)$

$3\mathrm{.}7.$ You are to decide between $3$ potential suppliers for an assembly for a product you are designing. After performing life testing on several assemblies, you find the following. What do you recommend? $(8$ Points$)$