A box in a supply room contains 24 light bulbs 8 are 13 watt 9 are 18 watt 7 are

Question

A box in a supply room contains 24 light bulbs 8 are 13 watt 9 are 18 watt 7 are 23 watt If bulbs are selected one by one until a 23 watt is obtained, what is the probability that it is necessary to examine at least 6 bulbs? A box in a supply room contains 24 light bulbs 8 are 13 watt 9 are 18 watt 7 are 23 watt If bulbs are selected one by one until a 23 watt is obtained, what is the probability that it is necessary to examine at least 6 bulbs? 8 are 13 watt 9 are 18 watt 7 are 23 watt If bulbs are selected one by one until a 23 watt is obtained, what is the probability that it is necessary to examine at least 6 bulbs?

Explanation / Answer

Total number of light bulbs= 24

To find,

P( X >=6) = 1 - P(X<6)

= 1 - [ P(X=1) +P(X=2)+P(X=3)+P(X=4)+P(X=5)]

Now, proability of getting 23 watt blub in 1st attempt is,

P(X=1) = 7/24 = 0.2917

Probility of getting 23 watt blub in 2nd attempt i.e. in 1st attempt getting 13 watt or 18 watt blub and in 2nd attempt getting 23 watt blub is,

P(X=2) = 17/24 * 7/23 = 0.2156

Probability of getting 23 watt blub in 3rd attempt is,

P(X=3) = 17/24 * 16/23 * 7/22 = 0.1568

Probability of getting 23 watt blub in 4th attempt is,

P(X=4) = 17/24 * 16/23 * 15/22 * 7/21 = 0.1120

Proability of getting 23 watt blub in 5tg attempt is,

P(X=5) = 17/24 * 16/23 * 15/22 * 14/21 * 7/20 = 0.0784

Thus,

P( X > = 6) = 1 - [ 0.2917 + 0.2156 + 0.1568 + 0.1120 + 0.0784] = 1 - 0.8545

P( X>= 6 ) = 0.1455

Therefore Proabability that it is necessary to examnine at least 6 blubs is 0.1455

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