Traffic checks on a certain section of highway suggest that 85 % of drivers are speeding there. Since 0.85 times 0.85 equals 0.7225 , the multiplication rule might suggest that there is approximately a 72 % chance that two vehicles in a row are both speeding. What's wrong with that reasoning?

Question

Christina Herrera

Mathematics

28 October, 02:48

Traffic checks on a certain section of highway suggest that 85 % of drivers are speeding there. Since 0.85 times 0.85 equals 0.7225 , the multiplication rule might suggest that there is approximately a 72 % chance that two vehicles in a row are both speeding. What's wrong with that reasoning?

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Answers (1)

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Skye Barron · Answer 1

The given events are not independent, therefore, multiplication rule cannot be applied.

Step-by-step explanation:

The multiplication rule is applicable only when the two events in consideration are independent. in other words, the probability of one event should not have any effect on the probability of the other event.

The multiplication rule is not applicable in the given scenario because these events are not independent. When the two vehicles are racing against each other then both vehicles will always be speeding which makes the probability of one vehicle dependent on the probability of another.