Math

QuestionA jar has 6 red marbles (1-6) and 8 blue marbles (1-8). Find the probabilities for these scenarios:
a) If a blue marble is chosen, what's the chance it's numbered 3? b) If a marble with number 1 is chosen, what's the chance it's blue?

Studdy Solution

STEP 1

Assumptions1. The jar contains6 red marbles, numbered1 to6. The jar also contains8 blue marbles, numbered1 to83. A marble is chosen at random, meaning each marble has an equal chance of being chosen4. If a marble is replaced, it has the same chance of being chosen again as any other marble

STEP 2

First, let's calculate the total number of marbles in the jar.
Totalmarbles=Numberofredmarbles+NumberofbluemarblesTotal\, marbles = Number\, of\, red\, marbles + Number\, of\, blue\, marbles

STEP 3

Now, plug in the given values for the number of red and blue marbles to calculate the total number of marbles.
Totalmarbles=6+8Total\, marbles =6 +8

STEP 4

Calculate the total number of marbles in the jar.
Totalmarbles=6+8=14Total\, marbles =6 +8 =14

STEP 5

For part a), we are told that the marble chosen is blue. Since there are8 blue marbles, each with a different number, the probability that the blue marble has the number3 on it is1 out of8.
(Bluemarbleis3)=1Numberofbluemarbles(Blue\, marble\, is\,3) = \frac{1}{Number\, of\, blue\, marbles}

STEP 6

Plug in the value for the number of blue marbles to calculate the probability.
(Bluemarbleis3)=18(Blue\, marble\, is\,3) = \frac{1}{8}

STEP 7

For part b), the first marble is replaced, and another marble is chosen at random. We are told that the marble has the number1 on it. There are2 marbles with the number1 on it (one red and one blue), so the probability that the marble is blue is1 out of2.
(MarbleisblueMarbleis1)=1Numberofmarbleswithnumber1(Marble\, is\, blue | Marble\, is\,1) = \frac{1}{Number\, of\, marbles\, with\, number\,1}

STEP 8

Plug in the value for the number of marbles with number1 to calculate the probability.
(MarbleisblueMarbleis1)=12(Marble\, is\, blue | Marble\, is\,1) = \frac{1}{2}So, the probability that a randomly chosen blue marble has the number3 on it is0.125, and the probability that a marble with the number1 on it is blue is0.5.

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