oniic7698
Answered

Maligayang pagdating sa Imhr.ca, kung saan maaari kang makakuha ng mga sagot mula sa mga eksperto nang mabilis at tumpak. Tuklasin ang malalim na mga sagot sa iyong mga tanong mula sa isang komunidad ng mga eksperto sa iba't ibang larangan. Kumuha ng detalyado at eksaktong sagot sa iyong mga tanong mula sa dedikadong komunidad ng mga eksperto sa aming 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

Salamat sa paggamit ng aming plataporma. Layunin naming magbigay ng tumpak at napapanahong mga sagot sa lahat ng iyong mga katanungan. Bumalik kaagad. Salamat sa pagpunta. Nagsusumikap kaming magbigay ng pinakamahusay na mga sagot para sa lahat ng iyong mga katanungan. Kita tayo muli sa susunod. Maraming salamat sa pagbisita sa Imhr.ca. Balik-balikan kami para sa pinakabagong mga sagot at impormasyon.