In a box containing $15$ bulbs, $5$ are defective. If $5$ bulbs are selected at random from the box, find the probability of the event, that
Only one of them is defective

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Solution

Good bulbs $= 10$ , Defective bulbs $= 5$
Total selections $=^{15} C_{5}$ ; ways of selecting
$1$ defective and $4$ good bulbs $=^{5} C_{1} \times^{10} C_{4}$
$\Rightarrow$ Probability $= 5 \times^{10} C_{4}^{15} C_{5}$ .

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In a box containing 15 bulbs, 5 are defective. If 5 bulbs are selected at random from the box, find the probability of the event, thatOnly one of them is defective

Good bulbs =10, Defective bulbs =5Total selections =15C5; ways of selecting1 defective and 4 good bulbs =5C1×10C4⇒ Probability =5×10C415C5.

In a box containing $15$ bulbs, $5$ are defective. If $5$ bulbs are selected at random from the box, find the probability of the event, that
Only one of them is defective

Good bulbs $= 10$ , Defective bulbs $= 5$
Total selections $=^{15} C_{5}$ ; ways of selecting
$1$ defective and $4$ good bulbs $=^{5} C_{1} \times^{10} C_{4}$
$\Rightarrow$ Probability $= 5 \times^{10} C_{4}^{15} C_{5}$ .