Pleaseeeee Helpppppppp!!!!!A bag contains five green marbles and seven yellow marbles. You randomly select three marbles. What is the probability that all three marbles are green when (a) you replace each marble before selecting the next marble, and (b) you do not replace each marble before selecting the next marble? Write each probability as a decimal rounded to the nearest thousandth. Then compare the probabilities.I don't know how to do this please help me!!!!

(a). The probability of picking a green marble is 5/12 because there are 5 green marbles and 12 marbles in total. Because we replace the marble, this is the probability for all three times we pick a marble. Now to find the total probability we need to times them together. We multiply because the two probabilities are independent of each other, one probability doesn't depend on another probability.

So the answer for (a) = 5/12 × 5/12 × 5/12 = 125/1728 = 0.072

(b). The probability that a green marble is picked the first time is 5/12, the probability that a green marble is picked the 2nd time is 4/11 because we don't replace the marble now we have one less green marble and one marble less in total. The probability that we pick a green marble the 3rd time is 3/10 again because we don't replace the marble. Again, these probabilities are independent so we multiply them.

So the answer for (b) = 5/12 × 4/11 × 3/10 = 60/1320 = 0.045

lisboa lisboa · Answer 2 · 2021-12-07T12:09:50+01:00

P(selecting three green marbles after replacing )=0.072

P(selecting three green marbles without replacing )=0.045

probability of selecting three green marbles after replacing is greater than the probability of selecting three green marbles without replacing

Given :

A bag contains five green marbles and seven yellow marbles. You randomly select three marbles.

There are 5 green marbles and seven yellow marbles.

Total marbles = 5+7=12 marbles

we need to select 3 marbles from 12 marbles

(a) all the three marbles are green and you replace each marbles before selecting the next marble

Probability of an event = number of events occurred by total outcomes

P(selecting first green )=[tex]\frac{5}{12}[/tex]

P(selecting second green )=[tex]\frac{5}{12}[/tex]

P(selecting third green )=[tex]\frac{5}{12}[/tex]

P(selecting three green marbles )=[tex]\frac{5}{12} \cdot \frac{5}{12} \cdot \frac{5}{12} =0.072[/tex]

(b) you do not replace each marble before selecting the next marble

P(selecting first green)=[tex]\frac{5}{12}[/tex]

P(selecting second green )=[tex]\frac{4}{11}[/tex]

P(selecting third green)=[tex]\frac{3}{10}[/tex]

P(selecting 3 green without replacing)=[tex]\frac{5}{12} \cdot \frac{4}{11} \codt \frac{3}{10}=0.045[/tex]

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