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## For consumers making purchases online, 60% have devices made by Apple, 85% own a smartphone, and 75% use Venmo. Also, out of the smartphone

Question

For consumers making purchases online, 60% have devices made by Apple, 85% own a smartphone, and 75% use Venmo. Also, out of the smartphone users, 80% use Venmo. Assume that having a device made by Apple and owning a smartphone are independent. A consumer who makes purchases online is selected at random, what is the probability they have an Apple device or own a smartphone (or both)? Enter your answer as a decimal to two places, and include the leading zero. For example, 0.12 would be a valid format.

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Mathematics
5 months
2021-09-04T12:18:43+00:00
2021-09-04T12:18:43+00:00 1 Answers
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## Answers ( )

Answer:The probability that a customer selected at random has an Apple device or own a smartphone or both is 0.94

Step-by-step explanation:The percentage of costumers that have a device made by Apple = 60%

The percentage of customers that own a smartphone = 85%

The percentage of customers that use Venmo = 80%

The percentage out of the smartphone users that use Venmo = 80%

The probability both independent events A and B occurring = P(A) × P(B)

The exclusive probability of A or B occurring P(A XOR B) = P(A) + P(B) – 2 × P(A ∩ B)

Therefore, the probability of A or B or both occurring is given as follows;

P(A or B or Both) = P(A) + P(B) – 2 × P(A ∩ B) + P(A) × P(B)

Where A represent the percentage of costumers that have a device made by Apple and let B represent the percentage of users that have a smartphone, we have;

P(A or B or Both) = 0.6 + 0.85 – 2×0.6×0.85 + 0.6 × 0.85 = 0.94

Therefore, the probability that a customer selected at random has an Apple device or own a smartphone (or both), P(A or B or Both) = 0.94