Question

The probability that a bulb produced by a factory will fuse after $100$ days of use is $0.05$. The probability that out of $5$ such bulbs none of them fuse after $100$ days is

• A. $1-{\left(\frac{19}{20}\right)}^5$
• B. ${\left(\frac{19}{20}\right)}^5$
• C. $1-{\left(\frac{1}{20}\right)}^5$
• D. ${\left(\frac{1}{20}\right)}^5$

Answer 1

The correct option is B ${\left(\frac{19}{20}\right)}^5$

Probability that bulb will fuse after 100 days $=0.05=\frac{1}{20}$
Probability that bulb will not fuse after 100 days $=1-\frac{1}{20}=\frac{19}{20}$
Probability that out of 5 such bulbs none of them fuse
${=}^5{C}_0\times (\frac{1}{20}{)}^0\times (\frac{19}{20}{)}^5=(\frac{19}{20}{)}^5$