Question

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?

Answer 1

#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

Answer 2

`\sf (1)/(24)=0.0417=4.17\%\:\:(3\:s.f.)`

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

`\sf Probability\:of\:an\:event\:occurring = (Number\:of\:ways\:it\:can\:occur)/(Total\:number\:of\:possible\:outcomes)`

Therefore:

`\sf P(white\:marble\:from\:Jar\:1)=(4)/(24)=(1)/(6)`

`\sf P(white\:marble\:from\:Jar\:2)=(20)/(80)=(1)/(4)`

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:

`\sf P(A\:and\:B)=P(A) \cdot P(B)`

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

`\sf P(white\:marble\:from\:Jar\:1)\:and\:\sf P(white\:marble\:from\:Jar\:2)=(1)/(6) \cdot (1)/(4)=(1)/(24)`