A radio station plays 24 minutes of music out of every 30 minutes. Write two ratios that are equivalent to the ratio 24/30
2 answers:
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P(B/A) is in the simplest form
Step-by-step explanation:
Let us explain how to solve the problem
- P(B|A) is called the "Conditional Probability" of B given A
- Conditional probability is the probability of one event occurring with some relationship to one or more other events that means event A has already happened, now what is the chance of event B
- The formula for conditional probability is P(B|A) = P(A and B)/P(A), where P(A and B) is P(A) . P(B given A occurred)
∵ There are 3 red marbles, 5 green marbles, and 2 blue
marbles in the jar
∴ The total number of the marbles in the jar = 3 + 5 + 2 = 10
∵ Two marbles are drawn from the bag, one after the other without
replacement
- That means red is already occurred when green is happened,
so it is a "Conditional Probability" of green given red
P(B/A) = P(A and B)/P(A)
∵ Event A is defined as drawing a red marble from the jar on
the first draw
∴ P(A) = P(red)
∵ P(red) =
∴ P(A) =
∵ Event B is defined as drawing a green marble on the second draw
∴ P(B) = P(green)
- The number of marbles after the red is chosen is 9
∵ P(green) =
∴ P(B) =
- Find P( A and B)
∴ P(A and B) = ( ) . (
)
∴ P(A and B) =
- Simplify the fraction by divide up and down by 15
∴ P(A and B) =
∵ P(B|A) = P(A and B)/P(A)
- Substitute the values of P(A and B) and P(A) in the rule above
∴ P(B/A) =
- Simplify the fraction
∵ ÷
=
×
=
- Divide up and down by 2
∴ P(B/A) =
P(B/A) is in the simplest form
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Answer: 90% decrease
Step-by-step explanation: First determine whether the number is increasing or decreasing. Since it changes from 2,000 to 200, it's going down so it's decreasing.
Now to find the percent decrease, we divide the
amount of change by the original number.
The <em>amount of change</em> is the difference between the two numbers
which in this case is 2,000 - 200 and the original number is 2,000.
.
2,000 - 200 is 1,800.
So we're left with 1,800/2,000 and dividing
2,000 into 1,800 gives us 0.9.
Remember however that our problem is
asking for a <em>percent</em>, not a decimal.
So we need to write 0.9 as a percent and we can do
that by multiplying it by 100 and adding the percent sign.
So 0.9 becomes 90%.
So when a number changes from 2,000 to 200,
it has decreased by 90%.