Question

The probability that an electronic device produced by a company does not function properly is equal to $0.1$. If $10$ devices are bought, then the probability, to the nearest thousand, that $7$ devices function properly is

• A. $2.057$
• B. $4.047$
  
• C. $1.057$
  
• D. $0.057$
  

Answer 1

The correct option is D $0.057$

This problem can be result using a Binomial distribution, in which we have

$n$ identical events with a probability $p$ of success.

The probability that $x$ of the $n$ events get success is given by:

$P\left(x\right)={}^n{C}_x\times p^x\times (1-p{)}^{n-x}$

Where, ${}^n{C}_x$ can be calculate as:

In this case there a $10$ device with a probability $0.9$ of function properly and we need to find the probability that $7$ of these device function properly, so replacing values, we get:

$P\left(7\right)={}^{10}{C}_7\times {0.9}^7\times (1-0.9{)}^{10-7}$

$P\left(7\right)=120\times 0.478\times 0.001$

$P\left(7\right)=0.057$

Finally the probability, to the nearest thousandth, that $7$ of the $10$ devices function properly is $0.057$.