Question

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

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.

Answer 1

A: Yes it's reasonable

B:`150` Times

Explanation:

`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