Let's say we had a bag of 10 marbles in which 3 are red. The probability of pulling out a red marble is 3/10 = 0.30 = 30%
If we do not replace that red marble, then there are 3-1 = 2 red marbles left and 10-1 = 9 marbles overall leftover. The probabiity of getting another red marble is 2/9 = 0.222 = 22.2% approximately. The probability has changed. The second event probability is dependent on the first event.
If we pulled out a non-red marble on the first selection, then we would have 3 red marbles out of 9 left over so 3/9 = 1/3 = 0.333 = 33.3% is the approximate probability of getting a red marble on the second selection. We see that this is not the same as the 30% we got earlier.
The second event depends entirely on what happens during the first event, so we say the second event is dependent on the first. Or more shortly, "the two events are dependent".
So any time there is the key phrase "no replacement" it means "dependent events".
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Based on what is discussed in the section above, this means that answer choices A and C are NOT independent events.
The other two answer choices do describe independent events. Why? Because the act of flipping a coin does not affect the outcome of the spinner, and vice versa. This is assuming the coin and spinner are kept separate. The probability for one item's outcome remains the same regardless of what happens to the other item's outcome. The same applies to rolling 4 number cubes (aka dice).
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<h3>Final Answers: Choice B and choice D</h3>
Given:
Principal = $1400
Simple rate of interest = 1.25%
Time = 6 month
To find:
The balance of the account after simple interest.
Solution:
The formula for simple interest is
Where, P is principal, r is the rate of interest in % and t is time in years.
Time = 6 months
= year
= 0.5 year
Putting 1400, r=1.25, t=0.5 years.
Now, the amount is
Therefore, the balance of the account after the simple interest is $1408.75.
We know that max eats 15 cookies in 2.5 hours
that mean he eats :
15/2.5 = 6 cookies in an hour
The amount of cookies that he eats in 4 hours would be :
6 x 4 = 24 cookies
Hope this helps
Answer:
6 days
Step-by-step explanation:
First we have to write an expression that represents Johnny's and Sal's banking plans.
Johnny: He has an initial value of $100 and that value will increase by $15 every day. So the expression looks like: 15x + 100, where x is the amount of days it's been.
Sal: An initial value of $250 and the value will decrease by $10 everyday. The expression looks like: -10x + 250, where x is the amount of days it's been.
To find how many days they have until they have the same amount of money in the bank, we can set the expressions equal to each other and solve for x:
15x + 100 = -10x + 250
Add 10x to both sides to isolate the x on one side of the equation:
25x + 100 = 250
Subtract 100 from both sides of the equation to isolate 25x:
25x = 150
Divide both sides by 25 to find the value of x:
x = 6
Since x represents the amount of days it's been, x = 6 means that it will take 6 days for their bank accounts to have the same amount of money in them.
Hope this helps :)