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 1 year ago
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