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QuestionWhat is the probability of drawing two blues in a row from a jar with 4 reds, 2 greens, and 6 blues?

Studdy Solution

STEP 1

Assumptions1. The jar contains4 red, green, and6 blue gumballs. . We are finding the probability of drawing two blue gumballs in a row without replacement.

STEP 2

First, we need to find the total number of gumballs in the jar. We can do this by adding the number of each color of gumballs.
Total gumballs=Reds+Greens+BluesTotal\, gumballs = Reds + Greens + Blues

STEP 3

Now, plug in the given values for the number of each color of gumballs to calculate the total number of gumballs.
Total gumballs=+2+6Total\, gumballs = +2 +6

STEP 4

Calculate the total number of gumballs.
Total gumballs=4+2+6=12Total\, gumballs =4 +2 +6 =12

STEP 5

Now we need to find the probability of drawing a blue gumball on the first draw. This is the number of blue gumballs divided by the total number of gumballs.
Probability of first blue=BluesTotal gumballsProbability\, of\, first\, blue = \frac{Blues}{Total\, gumballs}

STEP 6

Plug in the values for the number of blue gumballs and the total number of gumballs to calculate the probability of the first blue.
Probability of first blue=612Probability\, of\, first\, blue = \frac{6}{12}

STEP 7

Calculate the probability of the first blue.
Probability of first blue=612=12Probability\, of\, first\, blue = \frac{6}{12} = \frac{1}{2}

STEP 8

Since we are drawing without replacement, there is now one less blue gumball and one less gumball in total. We need to find the probability of drawing a blue gumball on the second draw.
Probability of second blue=Blues−1Total gumballs−1Probability\, of\, second\, blue = \frac{Blues -1}{Total\, gumballs -1}

STEP 9

Plug in the values for the number of blue gumballs and the total number of gumballs to calculate the probability of the second blue.
Probability of second blue=6−12−Probability\, of\, second\, blue = \frac{6 -}{12 -}

STEP 10

Calculate the probability of the second blue.
Probability of second blue=5Probability\, of\, second\, blue = \frac{5}{}

STEP 11

The probability of both events happening (drawing two blue gumballs in a row) is the product of the probabilities of each event.
Probability of two blues=Probability of first bluetimesProbability of second blueProbability\, of\, two\, blues = Probability\, of\, first\, blue \\times Probability\, of\, second\, blue

STEP 12

Plug in the values for the probability of the first blue and the probability of the second blue to calculate the probability of two blues.
Probability of two blues=2times511Probability\, of\, two\, blues = \frac{}{2} \\times \frac{5}{11}

STEP 13

Calculate the probability of two blues.
Probability of two blues=2times511=522Probability\, of\, two\, blues = \frac{}{2} \\times \frac{5}{11} = \frac{5}{22}The probability of getting two blues in a row without replacement is 5/225 /22.

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