A bag contains 9 red marbles and 4 purple marbles you selecta marble at random
a) What is the probability of selecting a red marble?
There are 9 red marbles out of a total of 13 marbles, so the probability of selecting a red marble is 9/13.
b) What is the probability of selecting a purple marble?
There are 4 purple marbles out of a total of 13 marbles, so the probability of selecting a purple marble is 4/13.
c) If you select a red marble, what is the probability of selecting another red marble on the second selection if the first marble is not replaced?
If the first marble is not replaced, there will be 8 red marbles left out of a total of 12 marbles. So, the probability of selecting another red marble is 8/12, which simplifies to 2/3.
d) If you select a purple marble, what is the probability of selecting another purple marble on the second selection if the first marble is not replaced?
If the first marble is not replaced, there will be 3 purple marbles left out of a total of 12 marbles. So, the probability of selecting another purple marble is 3/12, which simplifies to 1/4.
Teach me long division
Long division is a method used to divide two numbers that involve several steps. Here are the steps involved:
Step 1: Write the dividend (number to be divided) on top and the divisor (number to divide by) on the left.
Step 2: Divide the first digit of the dividend by the divisor. Write the quotient (the answer to the division) above the digit.
Step 3: Multiply the quotient by the divisor and write the product below the first digit of the dividend.
Step 4: Subtract the product from the first digit of the dividend and write the result below.
Step 5: Bring down the next digit from the dividend to the right of the remainder.
Step 6: Repeat steps 2 to 5 until you have written all the digits of the dividend.
Step 7: The quotient is the final answer.
Here’s an example of how to do long division:
Divide 221 by 13
Step 1: Write the dividend (221) on top and the divisor (13) on the left.
13 | 221
Step 2: Divide the first digit of the dividend (2) by the divisor (13). The quotient is 1.
13 | 221
1
Step 3: Multiply the quotient (1) by the divisor (13). The product is 13.
13 | 221
1
--
13
Step 4: Subtract the product (13) from the first digit of the dividend (2). The remainder is 9.
13 | 221
1
--
13
--
9
Step 5: Bring down the next digit of the dividend (2) to the right of the remainder (9).
13 | 221
1
--
13
--
9
2
Step 6: Divide the new number (92) by the divisor (13). The quotient is 7.
13 | 221
17
--
139
--
82
26
Step 7: Repeat step 6 until you’ve written all the digits of the dividend. The quotient is 17, with a remainder of 0.
13 | 221
17
--
139
--
82
--
39
--
0
So, the answer to 221 divided by 13 is 17.
To calculate the probability of selecting a specific color marble, you need to know the total number of marbles and the number of marbles of that specific color.
In this case, we have a bag containing 9 red marbles and 4 purple marbles. To find the probability of selecting a red marble at random, you divide the number of red marbles by the total number of marbles.
Total number of marbles = 9 red marbles + 4 purple marbles = 13 marbles
Probability of selecting a red marble = Number of red marbles / Total number of marbles
= 9 red marbles / 13 marbles
≈ 0.692 (rounded to three decimal places)
Therefore, the probability of selecting a red marble at random from this bag is approximately 0.692, or 69.2%.