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A box has 1 red marble, 3 blue marbles, and 4 green marbles. Maya draws a blue marble randomly from the box, replaces it, and then draws another marble randomly. What is the probability of drawing 2 blue marbles in a row? Explain

Sagot :

reinhard10158

Step-by-step explanation:

there are

1 red marble

3 blue marbles

4 green marbles

in the box.

that means there are 8 marbles in the box. which gives us 8 different outcomes for pulling randomly 1 marbles.

the probability for each of these 8 outcomes is equal : 1/8.

remember, the probability is always the number of desired cases over the number of total possible cases.

so, the probability of pulling a red marble is :

1 desired case

8 total cases

->

1/8 or 0.125

the probability of pulling a blue marble is :

3 desired cases

8 total cases

->

3/8 or 0.375

the probability of pulling a green marble is :

4 desired cases

8 total cases

->

4/8 = 1/2 or 0.5

now the experiment is pulling 2 marbles in a row, but the first pulled marble is put back into the box again.

this makes this a combined event, where the first AND the second event must fulfill the desired over total cases.

if the 2 events are independent (not overlapping or influencing each other), then we can simply multiply the probabilities. which is the case here, because the first marble is put back.

why ?

because now we have 8 possible outcomes for the first ball, and again 8 possible outcomes for the second ball, and when we combine all possibilities from the first with all possibilities from the second pull, we get 8×8 = 64 possible outcomes :

red. red

red. blue1

red. blue2

red. blue3

red. green1

...

green4 green4

so, the probability to pull a blue ball first is

3/8

and the probability to pull a blue ball second is

3/8 too

the combined probability of the combined event is

3/8 × 3/8 = 9/64

we have 3×3 = 9 desired outcomes of combining 3 blue and 3 blue balls out of the total of 64 possible outcomes.

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