oniic7698
Answered

Maligayang pagdating sa Imhr.ca, ang pinakamahusay na platform ng tanong at sagot para sa mabilis at tumpak na mga sagot. Maranasan ang kaginhawaan ng pagkuha ng mapagkakatiwalaang sagot sa iyong mga tanong mula sa isang malawak na network ng mga eksperto. Tuklasin ang malalim na mga sagot sa iyong mga tanong mula sa isang malawak na network ng mga propesyonal sa aming madaling gamitin na Q&A platform.

A box contains 10 blue, 5 yellow and 8 orange balls. Two balls are drawn at random. What is the probability that none of the ball is yellow?

Sagot :

Syubbana2

A box contains 10 blue, 5 yellow and 8 orange balls. Two balls are drawn at random. The probability that none of the balls is yellow is [tex]\frac{153}{253}[/tex].

To solve this problem you can use the combination and probability formulas.

The Combination Formulas:

C(n, r) = n! ÷ (n - r)! r!

C(n, r) = [tex]\frac{n!}{(n-r)!r!}[/tex]

*noted:

n = the number of items

r = how many items are taken at a time

The Probability Formulas:

p(A) = n(A) ÷ n(S)

p(A) = [tex]\frac{n(A)}{n(S)}[/tex]

*Noted:

P(A) = the probability of an event “A”

n(A) = the amount taken

n(S) = the total number of events in the sample space.

Step-by-step explanation:

Given:

  • Amount of blue balls is 10 balls
  • Amount of yellow balls is 5 balls
  • Amount of orange balls is 8 balls
  • Two balls are drawn at random.

Question:

What is the probability that none of the balls is yellow?

Solution:

Step 1

Find the number of ways to get two blue balls.

C(n, r) = n! ÷ (n - r)! r!

C(10, 2) = 10! ÷ (10 - 2)! 2!

C(10, 2) = 10! ÷ 8! 2!

C(10, 2) = (10 x 9 x 8!) ÷ (8! x 2!)

C(10, 2) = (10 x 9) ÷ (2 x 1)

C(10, 2) = 90 ÷ 2

C(10, 2) = 45

Step 2

Find the number of ways to get two orange balls.

C(n, r) = n! ÷ (n - r)! r!

C(10, 2) = 8! ÷ (8 - 2)! 2!

C(10, 2) = 8! ÷ 6! 2!

C(10, 2) = (8 x 7 x 6!) ÷ (6! x 2 x 1)

C(10, 2) = (8 x 7) ÷ (2 x 1)

C(10, 2) = 56 ÷ 2

C(10, 2) = 28

Step 3

Find the number of ways to get one blue ball and one orange ball.

C(n, r) + C(n, r)

= C(10, 1) + C(8, 1)

= (10! ÷ (10 - 1)! 1!) x (8! ÷ (8 - 1)! 1!)

= (10! ÷ 9! 1!) x (8! ÷ 7! 1!)

= ((10 x 9!) ÷ (9! x 1)) x ((8 x 7!) ÷ (7! x 1))

= (10 ÷ 1) x (8 ÷ 1)

= 10 x 8

= 80

Step 4

Find the number of ways to get two the balls that none balls is yellow.

⇔ The number of two the balls or none balls is yellow is the number of two blue balls or two orange balls or one blue balls and one orange balls

⇒ The number of two the balls or none balls is yellow = 45 + 28 + 80

⇒ The number of two the balls or none balls is yellow = 153

n(A) = 153

Step 5

Find the number of ways to get two the balls.

C(n, r) = n! ÷ (n - r)! r!

C(23, 2) = 23! ÷ (23 - 2)! 2!

C(10, 2) = 23! ÷ 21! 2!

C(10, 2) = (23 x 22 x 21!) ÷ (21! x 2!)

C(10, 2) = (23 x 22) ÷ (2 x 1)

C(10, 2) = 506 ÷ 2

C(10, 2) = 253

n(S) = 253

Step 6

Find the probability that none of the balls is yellow.

p(A) = n(A) ÷ n(S)

p(A) = [tex]\frac{n(A)}{n(S)}[/tex]

p(A) = [tex]\frac{153}{253}[/tex]

So, the probability that none of the balls is yellow is [tex]\frac{153}{253}[/tex]

Learn more about:

  • A pot has 6 shiny balls and 14 matte balls. If a ball is removed from the pot without replacement: brainly.ph/question/29163450

#SPJ1

Pinahahalagahan namin ang iyong oras sa aming site. Huwag mag-atubiling bumalik kailanman mayroon kang mga karagdagang tanong o kailangan ng karagdagang paglilinaw. Salamat sa iyong pagbisita. Kami ay nakatuon sa pagtulong sa iyong makahanap ng impormasyon na kailangan mo, anumang oras na kailangan mo ito. Maraming salamat sa paggamit ng Imhr.ca. Bumalik muli para sa karagdagang kaalaman mula sa aming mga eksperto.