A supermarket buys light globes (light bulbs) from three different manufacturers - Brightlight (35%), Glowglobe (20%) and Shinewell (45%). In the past, the supermarket has found that 1% of Brightlight's globes are faulty, and that 1.5% of each of Glowglobe's and Shinewell's globe are faulty. A customer buys a globe without looking at the manufacturer's name - in other words, it's random choice. When she gets home, she finds the globe is faulty. What is the probability she choose a Shinewell's globe?
Answers
Given : A supermarket buys light globes (light bulbs) from three different manufacturers -
Brightlight (35%), Glowglobe (20%) and Shinewell (45%).
In the past, the supermarket has found that 1% of Brightlight's globes are faulty, and that 1.5% of each of Glowglobe's and Shinewell's globe are faulty.
A customer buys a globe without looking at the manufacturer's name - in other words, it's random choice.
she finds the globe is faulty.
To Find : What is the probability she choose a Shinewell's globe?
Solution:
Assume that Total light bulb = 1000B
Brightlight = (35/100)1000B = 350B
Glowglobe = (20/100)1000B = 200B
Shinewell = (45/100)1000B = 450B
1% of Brightlight's globes are faulty, = (1/100)350B = 3.5B
1.5% of Glowglobe globes are faulty, = (1.5/100)200B = 3B
1.5% of Shinewell's globes are faulty, = (1.5/100)450B = 6.75B
Total Faulty = 3.5B + 3B + 6.75B = 13.25B
probability she choose a Shinewell's globe = 6.75B/ 13.25B
= 675/1325
= 27/53
= 0.5094
= 50.94 %
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