Question

In: Statistics and Probability

A box of 99 cellphones contains three yellow cellphones and six green cellphones. Complete parts​ (a)...

A box of 99 cellphones contains three yellow cellphones and six green cellphones. Complete parts​ (a) through​ (d) below.

a. If two cellphones are randomly selected from the box without​ replacement, what is the probability that both cellphones selected will be​ green?

b. If two cellphones are randomly selected from the box without​ replacement, what is the probability there will be one green cellphone and one yellow cellphone​ selected?

c. If three cellphones are selected with replacement​ (the first cellphone is returned to the box after it is​ selected), what is the probability that all three will be​ yellow?

d. If you were sampling with replacement​ (the first cellphone is returned to the box after it is​ selected), what would be the answers to​ (a) and​ (b)?

Solutions

Expert Solution

Number of yellow cell phones = 3

Number of green cell phones = 6

Total number of cell phones = 99

(a)

In case of selection without replacement,

Number of possible selections for selecting two cell phones

Number of possible selections for selecting two green cell phones

Required probability = 0.003092146

(b)

In case of selection without replacement,

Number of possible selections for selecting two cell phones

Number of possible selections for selecting one green cell phone and one yellow cell phone

Required probability = 0.003710575

(c)

In case of selection with replacement,

Number of possible selections for selecting three cell phones

Number of possible selections for selecting three yellow cell phones

Required probability = 0.00002782647

(d)

In case of selection with replacement,

For problem in (a)

Number of possible selections for selecting two cell phones

Number of possible selections for selecting two green cell phones

Required probability = 0.003673095

For problem in (b)

Number of possible selections for selecting two cell phones

Number of possible selections for selecting one green cell phone and one yellow cell phone

Required probability = 0.001836547

orchestra answered 2 years ago
Next > < Previous

Related Solutions

A box contains one yellow, two red, and three green balls. Two balls are randomly chosen...
A box contains one yellow, two red, and three green balls. Two balls are randomly chosen without replacement. Define the following events, and use them to find the conditional probabilities below. A:{A:{ One of the balls is yellow }} B:{B:{ At least one ball is red }} C:{C:{ Both balls are green }} D:{D:{ Both balls are of the same color }} a) P(B¯¯¯¯|A)= b) P(B¯¯¯¯|D)= c) P(C|D)= Suppose that E and F are events in the sample space with...
A box contains 4 orange pencils, 5 yellow pencils, and 3 green pencils. Two pencils are...
A box contains 4 orange pencils, 5 yellow pencils, and 3 green pencils. Two pencils are selected, one at a time, with replacement. Find the probability that the first pencil is green and the second pencil is yellow. Express your answer as a decimal, rounded to the nearest hundredth.
A box contains 4 red balls, 3 yellow balls, and 3 green balls. You will reach...
A box contains 4 red balls, 3 yellow balls, and 3 green balls. You will reach into the box and blindly select a ball, take it out, and then place it to one side. You will then repeat the experiment, without putting the first ball back. Calculate the probability that the two balls you selected include a yellow one and a green one. 3. Consider a binomially distributed random variable constructed from a series of 8 trials with a 60%...
Problem 1: A Six Sigma Green Belt randomly selects two parts from a box containing 5...
Problem 1: A Six Sigma Green Belt randomly selects two parts from a box containing 5 defective and 15 nondefective parts. He discards the box if one or both parts are defective. Using what you’re learned in chapter 3, what is the probability that he will select: One defective part Two defective parts Reject the box
Box A contains 6 red balls and 3 green balls, whereas box B contains 3 red...
Box A contains 6 red balls and 3 green balls, whereas box B contains 3 red ball and 15 green balls. Stage one. One box is selected at random in such a way that box A is selected with probability 1/5 and box B is selected with probability 4/5. Stage two. Finally, suppose that two balls are selected at random with replacement from the box selected at stage one. g) What is the probability that both balls are red? h)...
3. Box A contains 6 red balls and 3 green balls, whereas box B contains 3...
3. Box A contains 6 red balls and 3 green balls, whereas box B contains 3 red ball and 15 green balls. Stage one:One box is selected at random in such a way that box A is selected with probability 1/5 and box B is selected with probability 4/5. Stage two: First, suppose that 1 ball is selected at random from the box selected at stage one. a) What is the probability that the ball is red? b) Given that...
Box I contains three blue and two red marbles, Box II contains three blue and three...
Box I contains three blue and two red marbles, Box II contains three blue and three red marbles. Suppose one marble is drawn from Box I and placed in Box II and then one marble is drawn from Box II. Find the conditional probability that the marble drawn from Box I is blue given that the marble drawn from Box II is red.
A box contains 5 green marbles, 8 blue marbles, and 8 red marbles. Three marbles are...
A box contains 5 green marbles, 8 blue marbles, and 8 red marbles. Three marbles are selected at random from the box, one at a time, without replacement. Find the probability that the first two marbles selected are not red, and the last marble is red.
Box 1 contains 3 red balls, 5 green balls and 2 white balls. Box 2 contains...
Box 1 contains 3 red balls, 5 green balls and 2 white balls. Box 2 contains 5 red balls, 3 green balls and 1 white ball. One ball of unknown color is transferred from Box 1 to Box 2. (a) What is the probability that a ball drawn at random from Box 2 is green? (b) What is the probability that a ball drawn from Box 1 is not white?
We have 3 boxes. Box A contains 1 yellow ball and 2 red balls. Box B...
We have 3 boxes. Box A contains 1 yellow ball and 2 red balls. Box B conatins 2 yellow balls and 2 red balls. Box C contains 2 yellow balls and 1 red ball. First, we randomly choose between Box A and Box B. Then we randomly choose a ball from the selected box and put the ball into Box C. Lastly, we randomly choose a ball from Box C. Let E1 be the event that Box A is chosen...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT