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Delta Force
Delta Force asked in Science & MathematicsMathematics · 8 years ago

Statistics Help. Conditionally probability?

13.4% of text messages are spam. of all spam 17% contain both free and txt. of all non spam messagees 6% contain botht the word free and txt. Given that the message contains both free and txt, what is the probability it is spam?

I tried by creating a tree diagram. And got P(A &B)=(0.134)(0.17)=0.02278 and P(B), which is that the message contains both, =0.07474. Then, 0.02278/0.07474= ~30%.

However, the answer is actually 50%, how do they get this?

1 Answer

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  • David
    Lv 7
    8 years ago
    Favorite Answer

    .134 of all messages are spam

    .866 of all messages are not spam

    .134 * .17 = 0.02278 of all messages are spam that contain free and txt

    .134 * .83 = 0.11122 of all messages are spam that do not contain free and txt

    .866 * .06 = 0.05196 of all messages are not spam that contain free and txt

    .866 * .94 = 0.81404 of all messages are not spam that do not contain free and text

    given that the message contains free and txt

    .02278 + .05196

    0.07474

    what is the probability that it is spam

    .02278

    .02278 / .07474

    0.30478993845330478993845330478994

    30.48%

    you are correct

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