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
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