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    Find the probability of these events using basic probability principles

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    Suppose there are two types of Penn State Sports fans: Rabid (R), and Casual (R'). These fans either view a big game Live (L) or at Home (L'). Suppose 15% of Penn State fans are both Casual and watch the games at Home. If a fan watches at Home, the probability that he/she is Casual is 80%. Finally, suppose 10% of fans are Rabid.

    a. What is the probability of any fan watching the game at Home?

    b. If a fan watches the game Live, what is the probability that they are Rabid?

    © BrainMass Inc. brainmass.com December 24, 2021, 11:14 pm ad1c9bdddf
    https://brainmass.com/statistics/probability/find-probability-events-using-basic-probability-principles-550009

    SOLUTION This solution is FREE courtesy of BrainMass!

    Suppose there are two types of Penn State Sports fans: Rabid (R), and Casual (R'). These fans either view a big game Live (L) or at Home (L'). Suppose 15% of Penn State fans are both Casual and watch the games at Home. If a fan watches at Home, the probability that he/she is Casual is 80%. Finally, suppose 10% of fans are Rabid.

    R = Rabid P(R) = .10
    R'= Casual P(R') = 1 - .10 = .90

    L = Live
    L' = Home

    P(R'|L') = .80 P(R|L') = 1 - .80 = .20

    a. What is the probability of any fan watching the game at Home?

    P(R'|L') = .80

    P(R'L') = .15 = P(L')P(R'|L') = P(L')(.80)

    P(L') = (.15)/.80) = .1875

    b. If a fan watches the game Live, what is the probability that they are Rabid?

    Want P(R|L)

    P(R) = P(RL) + P(RL') = P(RL) + P(L')P(R|L')

    P(RL) = P(R) - P(L')P(R|L') = (.10) - (.1875)(.20) = .0625

    P(L) = 1 - P(L') = 1 - .1875 = .8125

    P(R|L) = P(RL)/P(L) = (.0625)/(.8125) = .0508

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    © BrainMass Inc. brainmass.com December 24, 2021, 11:14 pm ad1c9bdddf>
    https://brainmass.com/statistics/probability/find-probability-events-using-basic-probability-principles-550009

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