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Try this beautiful problem from Probability from AMC 8, 2004.

Spinners A and B are spun. On each spinner, the arrow is equally likely to land on each number. What is the probability that the product of the two spinners' numbers is even?

- \(\frac{2}{3}\)
- \(\frac{1}{3}\)
- \(\frac{1}{4}\)

probability

Equilly likely

Number counting

But try the problem first...

Answer: \(\frac{2}{3}\)

Source

Suggested Reading

AMC-8, 2004 problem 21

Challenges and Thrills in Pre College Mathematics

First hint

Even number comes from multiplying an even and even, even and odd, or odd and even

Can you now finish the problem ..........

Second Hint

A odd number only comes from multiplying an odd and odd..............

can you finish the problem........

Final Step

We know that even number comes from multiplying an even and even, even and odd, or odd and even

and also a odd number only comes from multiplying an odd and odd,

There are few cases to find the probability of spinning two odd numbers from 1

Multiply the independent probabilities of each spinner getting an odd number together and subtract it from 1 we get.......

\(1 - \frac{2}{4} \times \frac{2}{3}\)= \(1 - \frac{1}{3} = \frac{2}{3} \)

- https://www.cheenta.com/area-of-triangle-and-square-amc-8-2012-problem-25/
- https://www.youtube.com/watch?v=BXWGKh01nOw

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