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let L: room is locked k: he selects rite key to open a door then

p(L' and k) = p(L') +P(K)-P(L AND K) ALSO P(L') = 0.4 (GIVEN)

WHERE

P(K) = 0.375

S0,

p(L' and k) = 0.4 + 0.375 - (0.375 * 0.4)

= 0.625

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