Question

A box of flashlight batteries has 7 batteries, of which 4 are defective. If 2 batteries are selected at random without replacement, find the probability that both are defective.

Answer 1

Step 1

State an expression for the probability of an event.

`\text{Probability of an event occuring =}\frac{Number\text{ of required events}}{\text{Total number of events}}`

Number of required events = 4

Total number of events = 7

Step 2

Find the probabilities of defective batteries with replacement and without replacement

`\begin{gathered} \text{Probabilities with replacement =}(4)/(7) \\ \text{Probabilities without replacement =}(3)/(6) \end{gathered}`

Step 3

Find the probabilities that both are defective.

`(4)/(7)*(3)/(6)=(2)/(7)`

Hence the probability that 2 batteries selected at random without replacement are both defective is 2/7