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Probability Games!!!?

By admin Posted in: Uncategorized

1. A particular cell phone provider conducts an internal study of call failures. The study finds that 2% of calls fail to reach the network from the caller’s phone, 4% fail to be received by the second party’s phone, and 3% are the result of a failure in the network. What is the overall probability that a random cell phone call will fail to connect?
2. For extra security, a high school searches 15 random lockers each school day. If there are 740 students with lockers, what is the probability that a particular student’s locker gets searched at least once in a 20 day period?
3. A dinner party has 6 couples. The hostess wishes to seat all the guests around a circular table alternating males and females. How many differnt seating arrangements are there? Assume that there is no special seat around the table.

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  1. Elyasaf M Says

    1) 4%
    2) 1/15, if the same locker can be checked 2 times in that 20 day period
    3) 1

  2. M3 Says

    q1
    P[phone connects] = .98*.96*.97 = .912576 or 91.2576%
    so P[phone fails to connect] = 100 – 91.2576%
    = 8.7424%
    —————-
    q2
    P[particular locker not searched on a day]
    = 725/740
    = 145/148
    P[particular locker NOT searched even once in 20 days]
    = (145/148)^20
    P[particular locker searched at least once in 20 days]
    = 1 – (145/148)^20
    = 0.336 or 33.6%
    ————————-
    q3
    seat a lady anywhere.
    she becomes the reference point for all others
    seat the other ladies in the 5 alternate seats available for them in 5P5 = 5! ways
    seat the men in their seats in 6! ways
    total ways = 5!*6!
    = 86,400
    ————-

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