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One jar holds 20 green marbles and 4 white marbles. A second jar holds 60 black marbles and 20 white marbles. What is the probability that a white marble will be drawn from both jars?

Sagot :

Semsee45idn

Answer:

[tex]\sf \dfrac{1}{24}=0.0417=4.17\%\:\:(3\:s.f.)[/tex]

Step-by-step explanation:

Given information:

Contents of Jar 1:

  • 20 green marbles
  • 4 white marbles
  • total marbles = 20 + 4 = 24

Contents of Jar 2:

  • 60 black marbles
  • 20 white marbles
  • total marbles = 60 + 20 = 80

Probability Formula

[tex]\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}[/tex]

Therefore:

[tex]\sf P(white\:marble\:from\:Jar\:1)=\dfrac{4}{24}=\dfrac{1}{6}[/tex]

[tex]\sf P(white\:marble\:from\:Jar\:2)=\dfrac{20}{80}=\dfrac{1}{4}[/tex]

As the events are independent (i.e. drawing a marble from one jar does not influence or affect drawing a marble from the other jar), we can use the independent probability formula:

[tex]\sf P(A\:and\:B)=P(A) \cdot P(B)[/tex]

Therefore, the probability that a white marble will be drawn from both jars is:

[tex]\sf P(white\:marble\:from\:Jar\:1)\:and\:\sf P(white\:marble\:from\:Jar\:2)=\dfrac{1}{6} \cdot \dfrac{1}{4}=\dfrac{1}{24}[/tex]

#Jar 1

Total marbles =20+4=24

P(w)

  • 4/24=1/6

#Jar 2

Total marbles=60+20=80

P(w)

  • 20/80
  • 1/4

P(w in total)

  • 1/4(1/6)
  • 1/24
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