QuestionWhat is the probability of drawing a purple marble after keeping one orange marble from a jar with 8 purple and 3 orange marbles?

Studdy Solution

STEP 1

Assumptions1. There are8 purple marbles in the jar. There are3 orange marbles in the jar3. One orange marble is pulled and kept out of the jar4. One purple marble is pulled after the orange marble

STEP 2

First, we need to calculate the total number of marbles in the jar initially.
$Total\, marbles = Number\, of\, purple\, marbles + Number\, of\, orange\, marbles$

STEP 3

Now, plug in the given values for the number of purple and orange marbles to calculate the total number of marbles.
$Total\, marbles =8 +3$

STEP 4

Calculate the total number of marbles in the jar initially.
$Total\, marbles =8 +3 =11$

STEP 5

Next, we need to calculate the total number of marbles in the jar after one orange marble is pulled and kept out.
$Total\, marbles\, after\, pulling\, an\, orange\, marble = Total\, marbles -1$

STEP 6

Plug in the value for the total number of marbles to calculate the total number of marbles after pulling an orange marble.
$Total\, marbles\, after\, pulling\, an\, orange\, marble =11 -1$

STEP 7

Calculate the total number of marbles in the jar after pulling an orange marble.
$Total\, marbles\, after\, pulling\, an\, orange\, marble =11 -1 =10$

STEP 8

The probability of drawing a purple marble after pulling and keeping an orange marble is calculated by dividing the number of purple marbles by the total number of marbles after pulling an orange marble.
$Probability\, of\, drawing\, a\, purple\, marble = Number\, of\, purple\, marbles / Total\, marbles\, after\, pulling\, an\, orange\, marble$

STEP 9

Plug in the values for the number of purple marbles and the total number of marbles after pulling an orange marble to calculate the probability.
$Probability\, of\, drawing\, a\, purple\, marble =8 /$

STEP 10

Calculate the probability of drawing a purple marble.
$Probability\, of\, drawing\, a\, purple\, marble =8 /10 =0.8$ The probability of drawing a purple marble after pulling and keeping an orange marble is0.8.

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