Three prisoners, Kastur, Kevin, and Elijah, are in separate cells and sentenced to death. Zoethe governor has selected one of them at random to be pardoned. The warden, Andrew, knowswhich one is pardoned, but is not allowed to tell. Kastur begs Andrew to let her know theidentity of one of the two who are going to be executed. "If Kevin is going to be pardoned, give me Elijah’s name. If Elijah is going to be pardoned, give me Kevin’s name. And if I’mto be pardoned, secretly flip a coin to decide whether to name Kevin or Elijah."Andrew tells Kastur that Kevin is to be executed. Kastur is pleased because she believes thather probability of surviving has gone up from13to12, as it is now between her and Elijah. Kastur secretly tells Elijah the news, who reasons that Kastur’s chance of being pardoned isunchanged at13, but he is pleased, because his own chance of survival has gone up to23. Showthat Kastur is wrong about her new chances, but Elijah is right about his.

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Answer: question no. 1 -a. yes, the sides are in the ratio 2 : 5.question no. 2 -b. 59°question no. 3 -c. angles x and y are remote interior angles.question no. 4 -d. 90°, 45° and 45°question no. 5 -b. mn and qrstep-by-step explanation: question no. 1 -rs : xu = 3 : 7.5 = 2 : 5rt : x? = 6.4 : 16 = 2 : 5st : u? = 6 : 15 = 2 : 5as the ratios of all sides are equivalent, the triangles must be congruent and the sides must be proportional.therefore, the answer is: a. yes, the sides are in the ratio 2 : 5.question no. 2 -in the second diagram, angle b is the only letter not shown. therefore, the number must be equivalent to angle b.if we substitute the value of angle b as being 22° in the first diagram, we can now use the angle sum of a triangle to obtain the value of angle a.angle sum of a triangle = 180°therefore: let angle a = aa + 99 + 22 = 180a = 180 - 99 - 22a = 59°therefore, the answer is: b. 59°question no. 3 -angles x and y don't share the vertex of the triangle with the exterior angle w. remote interior angles don't share a vertex of a triangle with an exterior angle. this means that angles x and y are remote interior angles.therefore, the answer is: c. angles x and y are remote interior angles.question no. 4 -the sum of all interior angles of a triangle must be equivalent to 180°.90°, 45° and 45° are the only set of angle measures that are equivalent to 180°.therefore, the answer is: d. 90°, 45° and 45°question no. 5 -the only pair of sides stated in the options which are corresponding are mn and qr.therefore, the answer is: b. mn and qr.