Question

Please help! Correct answer only!

Lester teaches a ceramics class on the weekends. In Sunday's class, the students created 19 clay objects, 12 of which were vases. After each class, Lester bakes the clay objects in a hot kiln to harden them. Students pick up their finished pieces later in the week.
If Lester randomly chose 16 clay objects to bake in the kiln Sunday night, what is the probability that exactly 11 of the chosen clay objects are vases?

Write your answer as a decimal rounded to four decimal places.

Answer 1

The probability that exactly 11 of the chosen clay objects are vases

P(X = 11 ) = 0.16472

Explanation:

Step(i):-

Given students created 19 clay objects, 12 of which were vases

probability of successes

`p = (x)/(n) = (12)/(19) = 0.6315`

q = 1 - p = 1 - 0.6315 = 0.3685

Step(ii):-

Given n = 16

Let 'X' be the random variable in binomial distribution

`P(X = r) = n _{C_(r) } p^(r) q^(n-r)`

The probability that exactly 11 of the chosen clay objects are vases

`P(X = 11) = 16 _{C_(11) } (0.6315)^(11) (0.3585)^(16-11)`

we will use formula

`n_{C_(r) } = (n!)/((n-r)!r!)`

`n_{C_(r) } =n_{C_(n-r) }`

`16_{C_(11) } =16_{C_(16-11) }= 16_{C_(5) } = (16 X 15 X 14 X 13 X 12)/(5 X 4 X 3 X 2 X 1) = 4368`

`P(X = 11) = 4368 (0.006369)(0.005921)`

P(X = 11 ) = 0.16472

Conclusion:-

The probability that exactly 11 of the chosen clay objects are vases

P(X = 11 ) = 0.16472