An upscale sari shop stocks only silk and cotton handloom saris. Customers are found to buy silk sari with probability 45% and cotton sari with probability 75%. If 5% of the customers do not buy anything, then what proportion buys both cotton and silk sari?
Answers
Given : An upscale sari shop stocks only silk and cotton handloom saris. Customers are found to buy silk sari with probability 45% and cotton sari with probability 75%. 5% of the customers do not buy anything,
To Find : what proportion buys both cotton and silk sari
Solution:
buy silk sari with probability 45%
=> buy silk sari with proportion S = 0.45
cotton sari with probability 75%.
=> cotton sari with proportion C = 0.75
Buy none = 5 %
Buy none proportion = 0.05
proportion buys both cotton and silk sari C ∩ S = ?
Total = 1
Total = S + C - C ∩ S + None
1 = 0.45 + 0.75 - C ∩ S + 0.05
=> C ∩ S = 0.25
proportion buys both cotton and silk sari = 0.25
25 %
buys both cotton and silk sari = 25 % or 0.25
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