Ava teaches a ceramics class on the weekends. In Sunday's class, the students created 7 clay objects, 5 of which were plates. After each class, Ava bakes the clay objects in a hot kiln to harden them. Students pick up their finished pieces later in the week. If Ava randomly chose 4 clay objects to bake in the kiln Sunday night, what is the probability that all of them are plates ? Write your answer as a decimal rounded to four decimal places.

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HaedenS289450 HaedenS289450 · Answer 1 · 2022-10-26T10:04:16+02:00

Given data:

7 clay objects out of which 5 are plates

If Ava randomly chose 4 clay objects to bake in the kiln Sunday night.

These are the possibilities:

At the first selection: 5 plates out of 7 clay objects will be selected

At the second selection: The number of plates will be reduced to 4 plates and the number of clay objects will now be 6

Similarly, at the third selection, 3 plates will be selected from 5 clay objects

At the fourth selection, 2 plates will be selected from 4 clay objects.

Therefore the probability that all 4 of them are plates will be:

[tex]\frac{5}{7}\times\frac{4}{6}\times\frac{3}{5}\times\frac{2}{4}[/tex]

=>

[tex]\frac{120}{840}=\frac{1}{7}[/tex]

=>

[tex]\frac{1}{7}=0.1429[/tex]

Answer = 0.1429