A survey is made to determine the number of households having electric appliances in a certain city. It is found that 75% have radios (R), 65% have electric irons (I), 55% have electric toasters (T), 50% have irons and radios, 40% have radios and toasters, 30% have irons and toasters, and 20% have all three. Determine the probability that a household has at least one of these appliances

Question

Mathematics

Nitro

25 January, 14:16

A survey is made to determine the number of households having electric appliances in a certain city. It is found that 75% have radios (R), 65% have electric irons (I), 55% have electric toasters (T), 50% have irons and radios, 40% have radios and toasters, 30% have irons and toasters, and 20% have all three. Determine the probability that a household has at least one of these appliances

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Luke · Answer 1

The probability that a household has at least one of these appliances is 0.95

Step-by-step explanation:

Percentage of households having radios P (R) = 75% = 0.75

Percentage of households having electric irons P (I) = 65% = 0.65

Percentage of households having electric toasters P (T) = 55% = 0.55

Percentage of household having iron and radio P (I∩R) = 50% = 0.5

Percentage of household having radios and toasters P (R∩T) = 40% = 0.40

Percentage of household having iron and toasters P (I∩T) = 30% = 0.30

Percentage of household having all three P (I∩R∩T) = 20% = 0.20

Probability of households having at least one of the appliance can be calculated using the rule:

P (at least one of the three) = P (R) + P (I) + P (T) - P (I∩R) - P (R∩T) - P (I∩T) + P (I∩R∩T)

P (at least one of the three) = 0.75 + 0.65 + 0.55 - 0.50 - 0.40 - 0.30 + 0.20 P (at least one of the three) = 0.95

The probability that a household has at least one of these appliances is 0.95