Sheldon uses the even numbered cubes below to play a game. 2 , 4 , 6 , 8 and 10. ? Rest of problem is in Details!

Question

Sheldon uses the even numbered cubes below to play a game.
Part A : Sheldon randomly selects a cube 100 times and replaces it. Is it reasonable to expect Sheldon to choose a number that is less than 6 about 50 times? Show work!

Part B : Sheldon uses the same process to select a cube 250 times. How many times should he expect to choose the cubes labeled 6, 8, or 10? Justify your reasoning.

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Answer 1 · 2018-04-20T12:53:05

A: Yes it's reasonable

B:#150# Times

#S={2,4,6,8,10}#

#color(blue) (Part (A):#

Let #C# be the event of the appearance of a number less than #6#

#C={2,4}#

so #P(A)=N_C/N_S#

#color(green)("Where " N_C" is the number of elements of " C=2)#

#color(green)("And " N_S" is the number of elements of " S=5)#

#P(C)=2/5=0.4#

so the probability that #C# occurs is #40%#

so if He selects a cube 100 times then he will get 40 cubes with the number #2,4#

but since the question is asking if it's reasonable if He got 50 cubes?

I would say Yes it's reasonable since 50 cubes is near 40

#color(blue)(Part(B)#

Let #V# be the event of the appearance of #6,8,10#

#V={6,8,10}#

#P(V)=N_V/N_S#

#P(V)=3/5=0.6#

In order to calculate how many times he got a cube labeled #6,8,10# when He drew 250 cubes

#color(green)("Number of Occuring of " (V)= P(V)xx" Number of draws"#

#250xx0.6=150# Times

I will put this on double check to make sure #Part(A)# is correct