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3 years ago

The number name for 6.837 is

Mathematics

1 answer:

Vsevolod [243]3 years ago

7 0

Six and eighty hundred thirty seven thousandths

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3 years ago

You are playing a game called Tsunami Duck Pond. In Tsunami Duck Pond there are 100 ducks that get pummeled by tidal waves. You

lilavasa [31]

Answer:

a) W is a binomial random variable because in each trial there are only two possible outcomes, and the probability of a success is always the same.

b) 0.2013 = 20.13% probability that you win exactly 3 times.

Step-by-step explanation:

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

a. Explain why W is a binomial random variable.

For each time a duck is selected, there are only two possible outcomes. Either it has a star, or it does not. Also, after a duck is selected, it is placed back in the water which means that in each trial, the probability of finding a duck with star is the same. This is why W is a binomial random variable.

b. Find the probability that you win exactly 3 times.

Let W=the number of times you win if you play this game 10 times.

This means that $n = 10$

The game claims to have 20 ducks with stars among the 100 ducks.

This means that $p = \frac{20}{100} = 0.2$

We have to find P(X = 3). So

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 3) = C_{10,3}.(0.2)^{3}.(0.8)^{7} = 0.2013$

0.2013 = 20.13% probability that you win exactly 3 times.

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3 years ago