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Let n stand for the number. Evaluate the expreesion

Sedaia [141]

Where is the expression?

8 0

3 years ago

You’ve bought a half-dozen (six) eggs from the store but you forgot to check them first! The probability that no eggs are broken

GREYUIT [131]

Answer:

a)

$P(X = 0) = C_{6,0}.(0.1416)^{0}.(0.8584)^{6} = 0.4$

$P(X = 1) = C_{6,1}.(0.1416)^{1}.(8584)^{5} = 0.3960$

$P(X = 2) = C_{6,2}.(0.1416)^{2}.(8584)^{4} = 0.1633$

$P(X = 3) = C_{6,3}.(0.1416)^{3}.(8584)^{3} = 0.0359$

$P(X = 4) = C_{6,4}.(0.1416)^{4}.(8584)^{2} = 0.0044$

$P(X = 5) = C_{6,5}.(0.1416)^{5}.(8584)^{1} = 0.0003$

$P(X = 6) = C_{6,6}.(0.1416)^{6}.(8584)^{0} = 0.00001$

b) 56.77% probability that an even number of eggs is broken.

c)

Expectation: 0.8496

Variance: 0.7293

Step-by-step explanation:

For each egg, there are only two possible outcomes. Either it is broken, or it is not. The probability of an egg being broken is independent from other eggs. So we use the binomial probability distribution to solve this question.

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.

The expected value of the binomial distribution is:

$E(X) = np$

The variance of the binomial distribution is:

$V(X) = np(1-p)$

There are 6 eggs

So $n = 6$

The probability that no eggs are broken is 0.4.

This means that $P(X = 0) = 0.4$ . So

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

$P(X = 0) = C_{6,0}.p^{0}.(1-p)^{6}$

$(1 - p)^{6} = 0.4$

Taking the sixth root from both sides of the equality

$(1 - p) = 0.8584$

p = 0.1416

Each egg has a 0.1416 probability of being broken

(a) Write out the pmf of X.

Probability of each value, from 0 to 6

$P(X = 0) = C_{6,0}.(0.1416)^{0}.(0.8584)^{6} = 0.4$

$P(X = 1) = C_{6,1}.(0.1416)^{1}.(8584)^{5} = 0.3960$

$P(X = 2) = C_{6,2}.(0.1416)^{2}.(8584)^{4} = 0.1633$

$P(X = 3) = C_{6,3}.(0.1416)^{3}.(8584)^{3} = 0.0359$

$P(X = 4) = C_{6,4}.(0.1416)^{4}.(8584)^{2} = 0.0044$

$P(X = 5) = C_{6,5}.(0.1416)^{5}.(8584)^{1} = 0.0003$

$P(X = 6) = C_{6,6}.(0.1416)^{6}.(8584)^{0} = 0.00001$

(b) Compute the probability that an even number of eggs is broken.

0, 2, 4 or 6

$P = P(X = 0) + P(X = 2) + P(X = 4) + P(X = 6) = 0.4 + 0.1633 + 0.0044 + 0.00001 = 0.5677$

56.77% probability that an even number of eggs is broken.

(c) Compute the expectation and variance of X.

Expectation:

$E(X) = np = 6*0.1416 = 0.8496$

Variance:

$V(X) = np(1-p) = 6*0.1416*0.8584 = 0.7293$

7 0

4 years ago

when solving an equation, which is the best first step to begin to simplify the equation? -2(x+3)=-10

alekssr [168]

Answer: Following the rules of PEMDAS, you want to divide both sides of the equation by -2. This would change your equation to x+3=5. Then you move your constant to the right-hand side and change its sign. Your equation is now x=5-3. subtract 5-3 and your answer is x=2.

6 0

3 years ago

Determine x and y knowing that 2y +2x =257

m_a_m_a [10]

\left[y \right] = \left[ \frac{257}{2}-x\right][y]=[2257−x] . totally answer

3 0

3 years ago

What 14/27 divided by 7 in simplest for <br> I will brain if right

tamaranim1 [39]

Answer:

0. 074

Step-by-step explanation:

6 0

3 years ago