Question

An employee at a department store is stocking cell phone cases. He has a box of 80 cases. Among the 80 cases, 40 are black, 10 are white, and 30 are pink.
If he reaches into the bag randomly and removes one at a time, what is the probability that the first three cases are all pink?
please show your work. HELPP ASAP please.

Answer 1

Answer:

$\sf \dfrac{203}{4108}$

As a decimal = 0.05 (nearest hundredth)

Step-by-step explanation:

$\sf Probability \ of \ an \ event \ occurring = \dfrac{Number \ of \ ways \ it \ can \ occur}{Total \ number \ of \ possible \ outcomes}$

First pick:

$\sf \implies P(pink)=\dfrac{30}{80}$

As the case is NOT replaced, second pick:

$\sf \implies P(pink)=\dfrac{30-1}{80-1}=\dfrac{29}{79}$

As the case is NOT replaced, third pick:

$\sf \implies P(pink)=\dfrac{29-1}{79-1}=\dfrac{28}{78}$

Therefore,

$\sf \implies P(pink \ and \ pink \ and \ pink)=\dfrac{30}{80} \times \dfrac{29}{79} \times \dfrac{28}{78}=\dfrac{203}{4108}$

Answer as a decimal = 0.05 (nearest hundredth)