In a survey of 100 individuals who use one of two brands of

In a survey of 100 individuals who use one of two brands of detergent, 43 used brand A, 37 used brand B, and 20 used both brands A and B.

a) What proportion (probability) used either brand A or B?

b) What proportion used neither of these two brands?

Please make the final answer in bold so I can easily find it

Solution

a)

Note that

P(A or B) = P(A) + P(B) - P(A and B)

= 43/100 + 37/100 - 20/100

= 0.6 [ANSWER]

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b)

P(not A nor B) = 1 - P(A or B)

= 1 - 0.6

= 0.4 [ANSWER]