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There are 5 dice in a bag: two tetrahedrons (4-sided), one cube (6-sided), and t

ID: 3205872 • Letter: T

Question

There are 5 dice in a bag: two tetrahedrons (4-sided), one cube (6-sided), and two octahedrons (8-sided). I grab a dice at random (i.e., the probability of picking any dice is 1/5) and roll it. (a) What is the probability of picking an octahedron? (b) Suppose I tell you that the result of the roll is a 3, what is the probability that the dice I picked is a tetrahedron? (c) Which dice is most likely if I tell you that the result of the dice is a 6? A tetrahedron, a cube, or an octahedron? (d) Which dice is most likely if I tell you that the result of the dice is a 7?

Explanation / Answer

There are 5 dice :

2 Octahedrons

1 Cube

2 Tetra hedrons

each of being picked with a probability of 0.2 , or equiproabable

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1) Probability of picking a octahedron

= 2C1 / 5C1 ( any one octahedron of two available / 1 out of 5 )

=0.4

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2) since 3 is present once in all dice

the approach is similiar to picking a dice

in this case pciking a tetrahedron

= 2C1 /5C1

=0.4

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3) if the result is 6 , there is 0.4 probability of it being a octagedron , 0.2 being a cube , and 0.4 of being a tetrahedron .the approach is similair to part 1 ,2

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4) if the result is a 7 , its 100% a octahedron since only it contains numbers from 1-8