20 marbles in a bag. 4 are red, 5 are blue, 5 are black, 4 are white and 2 are yellow. What is the probability that he pulls out
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Answer:
P=0.125
If it is repeated 10,000, it is expected "3 tails in a row" about 1,250 times.
Step-by-step explanation:
When flipping a coin a number of times, we can modeled this as a random variable with a binomial distribution.
In this case, we have to calculate the probability of 3 consecutive tails. If we define p as the probability of getting a tail (which has a value of p=0.5 if it is an unbiased coin), the probability of getting 3 tails in a row is:
If that event of "flipping a coin 3 times" is repeated 10,000 times, we can expect to have 3 tails in a row about 1,250 times:
because we expect 0.125 events of this type for every try, so we can multiply this probability (or expected frequency) by the number of trials and we get the expected number of events described.
We have been given that you invest $100,000 in an account earning 8% interest compounded annually. We are asked to find the time it will take the amount to reach $300,000.
We will use compound interest formula to solve our given problem.
, where,
A = Final amount after t years,
P = Principal amount,
r = Annual interest rate in decimal form,
n = Number of times interest is compounded per year,
t = Time in years.
Let us take natural log on both sides of equation.
Using natural log property , we will get:
Upon rounding to nearest tenth of year, we will get:
Therefore, it will take approximately 14.3 years until the account holds $300,000.