# All use computer

It is reported that 72% of working women use computers at work. Choose 3 women at random, find the probability that all 3 women use a computer in their jobs.

Result

p =  0.373

#### Solution:

$q=72 \%=\dfrac{ 72 }{ 100 }=0.72 \ \\ \ \\ C_{{ 3}}(3)=\dbinom{ 3}{ 3}=\dfrac{ 3! }{ 3!(3-3)!}=\dfrac{ 1 } { 1 }=1 \ \\ \ \\ p={ { 3 } \choose 3 } \cdot \ q^3 \cdot \ (1-q)^{ 3-3 }=1 \cdot \ 0.72^3 \cdot \ (1-0.72)^{ 3-3 } \doteq 0.3732 \doteq 0.373 \ \\ \ \\ \text{ Correctness test: } \ \\ \ \\ p_{2}=q^3=0.72^3 \doteq 0.3732$

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