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Probability Question

Rebecca has 9 cards, each with a number on them. The numbers are:
2, 2, 3, 4, 5, 6, 6, 7, 9

She picks three cards at random without replacement. Rebecca multiplies three numbers to get a score.

Calculate the probability that the score is an even number.

I think the answer is 20/21 but I don't know how to get it, can someone help?
I thought of doing probability trees but with 9 numbers that would take wayyy too long.
Where O = Odd and E = Even you need to consider that OOO= O, OOE = E, OEE = E and EEE = E. You will notice that all outcomes give an even number with the exception of OOO and thus the probability of XYZ = E is equal to 1 - (The probability that XYZ = O). There are 4 odd numbers = 3,5,7,9. So the probability of picking 3 odd numbers OOO = 4/9 * 3/8 * 2/7 = 1/21. And thus 1 - 1/21 = 20/21 = Probability that the product of XYZ is even.
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angela_12
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Original post by UserMaths01
Where O = Odd and E = Even you need to consider that OOO= O, OOE = E, OEE = E and EEE = E. You will notice that all outcomes give an even number with the exception of OOO and thus the probability of XYZ = E is equal to 1 - (The probability that XYZ = O). There are 4 odd numbers = 3,5,7,9. So the probability of picking 3 odd numbers OOO = 4/9 * 3/8 * 2/7 = 1/21. And thus 1 - 1/21 = 20/21 = Probability that the product of XYZ is even.


That seems so obvious now! Thank-you x

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