3 bulbs are defective in a box of 10 bulbs. 2 bulbs are randomly selec

1.	3 bulbs are defective in a box of 10 bulbs. 2 bulbs are randomly selected from this box. These bulbs are fixed in two bulb-holders installed in a room. Find the probability that the room will be lighted after starting the electric supply.
Answer» 3 bulbs are defective in a box of 10 bulbs. ∴ 7 bulbs are non-defective. Total number of primary outcomes of selecting 2 bulbs randomly from 10 bulbs is, n = ¹⁰C₂ = \(\frac{10×9}{2×1}\) = 45A = Event that the room will be lighted after starting the electric supply. There are two options of occurring event A: If 2 bulbs are non-defective and are fixed in the first bulb holder. OR If in 2 bulbs one bulb is non-defective and one bulb Is defective and are fixed in the second bulb holder. ∴ Favourable outcomes for event A is, m = ⁷C₂ + ⁷C₁ × ³C₁ = \(\frac{7×C}{2×1} \)+ ( 7 × 3) = 21 + 21 = 42 ∴ p(A) = \(\frac{m}{n} = \frac{42}{45} = \frac{14}{15}\)

3 bulbs are defective in a box of 10 bulbs. 2 bulbs are randomly selected from this box. These bulbs are fixed in two bulb-holders installed in a room. Find the probability that the room will be lighted after starting the electric supply.

Answer»

3 bulbs are defective in a box of 10 bulbs.

∴ 7 bulbs are non-defective.

Total number of primary outcomes of selecting 2 bulbs randomly from 10 bulbs is,

n = ¹⁰C₂ = \(\frac{10×9}{2×1}\) = 45A = Event that the room will be lighted after

starting the electric supply.

There are two options of occurring event A:

If 2 bulbs are non-defective and are fixed in the first bulb holder.

If in 2 bulbs one bulb is non-defective and one bulb Is defective and are fixed in the second bulb holder.

∴ Favourable outcomes for event A is,

m = ⁷C₂ + ⁷C₁ × ³C₁

= \(\frac{7×C}{2×1} \)+ ( 7 × 3)

= 21 + 21 = 42

∴ p(A) = \(\frac{m}{n} = \frac{42}{45} = \frac{14}{15}\)

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