Question

a flashlight has 8 batteries out of which 3 are dead if two batteries are selected without replacement and tested find the probability that both her dead

Answer 1

3 /8 is the probability

Answer 2

The probability that both the batteries will be dead is $\bold{\frac{3}{28}}$

Given:  

A flash light contains 8 batteries and among 8 batteries 3 batteries are dead.

To find:

The probability where both the batteries will be dead

Solution:

Total number of batteries = 8

Number of dead batteries = 3

Number of working batteries = 8 – 3 = 5

Let D be the event of selecting 2 dead batteries.

Let F be the event of selecting the first dead battery.

Probability of selecting the 1st dead battery i.e. $\mathrm{P}(\mathrm{F})=\frac{\text { Number of dead batteries }}{\text {Total number of batteries}}=\frac{3}{8}$

Number of remaining batteries = 8 – 1 = 7

Let S be the event of selecting the 2nd dead battery without replacement.

Probability of selecting the 2nd dead battery i.e.$P(S)=\frac{\text {Number of dead batteries}}{\text {Total number of batteries}}=\frac{2}{7}$

∴ Probability of selecting 2 dead batteries $\mathrm{P}(\mathrm{D})=\frac{3}{8} \times \frac{2}{7}=\frac{3}{28}$