Mathematics, 23.01.2020 05:31 delaneymoses21

the one-time fling! have you ever purchased an article of clothing (dress, sports jacket, worn the item once to a party, and then returned the purchase? this is called a one-time fling. about 5% of all adults deliberately do a one-time fling and feel no guilt about it! in a group of nine adult friends, what is the probability of the following? (round your answers to three decimal places.) answer the following:

a. no one has done a one time fling

b. at least one person has done a one time fling

c. no more than two people have done a one time fling

Answers: 2

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Answer from: bellrivera3434

a) There is a 63.02% probability that no one has done an one time fling.

b) There is a 36.98% probability that at least one person has done a one time fling

c) There is a 99.15% pprobability that no more than two people have done a one time fling.

Step-by-step explanation:

For each adult, there are only two possible outcomes. Either they have done an one time fling, or they have not. This means that we use the binomial probability distribution to solve this problem.

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 combinatios 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.

In this problem we have that:

n = 9, p = 0.05

A. no one has done a one time fling

This is P(X = 0).

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

$P(X = 0) = C_{9,0}.(0.05)^{0}.(0.95)^{9} = 0.6302$

There is a 63.02% probability that no one has done an one time fling.

B. at least one person has done a one time fling

Either no one has done a one time fling, or at least one person has. The sum of the probabilities of these events is decimal 1.

$P(X = 0) + P(X \geq 1) = 1$

$P(X \geq 1) = 1 - `(X = 0) = 1 - 0.6302 = 0.3698$

There is a 36.98% probability that at least one person has done a one time fling

c. no more than two people have done a one time fling

This is

$P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)$

$P(X = 1) = C_{9,1}.(0.05)^{1}.(0.95)^{8} = 0.2985$

$P(X = 2) = C_{9,2}.(0.05)^{2}.(0.95)^{7} = 0.0628$

$P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.6302 + 0.2985 + 0.0628 = 0.9915$

There is a 99.15% pprobability that no more than two people have done a one time fling.

Answer from: Quest

step-by-step explanation:

milk=16 large

soda=280 kids

juice box=82 regular

63 soda +63 regular

124 large total

Answer from: Quest

Answer: question no. 1 -a. yes, the sides are in the ratio 2 : 5.question no. 2 -b. 59°question no. 3 -c. angles x and y are remote interior angles.question no. 4 -d. 90°, 45° and 45°question no. 5 -b. mn and qrstep-by-step explanation: question no. 1 -rs : xu = 3 : 7.5 = 2 : 5rt : x? = 6.4 : 16 = 2 : 5st : u? = 6 : 15 = 2 : 5as the ratios of all sides are equivalent, the triangles must be congruent and the sides must be proportional.therefore, the answer is: a. yes, the sides are in the ratio 2 : 5.question no. 2 -in the second diagram, angle b is the only letter not shown. therefore, the number must be equivalent to angle b.if we substitute the value of angle b as being 22° in the first diagram, we can now use the angle sum of a triangle to obtain the value of angle a.angle sum of a triangle = 180°therefore: let angle a = aa + 99 + 22 = 180a = 180 - 99 - 22a = 59°therefore, the answer is: b. 59°question no. 3 -angles x and y don't share the vertex of the triangle with the exterior angle w. remote interior angles don't share a vertex of a triangle with an exterior angle. this means that angles x and y are remote interior angles.therefore, the answer is: c. angles x and y are remote interior angles.question no. 4 -the sum of all interior angles of a triangle must be equivalent to 180°.90°, 45° and 45° are the only set of angle measures that are equivalent to 180°.therefore, the answer is: d. 90°, 45° and 45°question no. 5 -the only pair of sides stated in the options which are corresponding are mn and qr.therefore, the answer is: b. mn and qr.

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