F.3 Probability

1) Jenny takes either a route 6C or 6F bus from Kowloon City Pier to school at Yaumatei. These two routes both leave the terminus every 20 minutes. If a route 6F bus leaves the terminus 7 minutes after a route 6C bus leaves, what is the probability that Jenny takes a route 6C bus to school?

2) Number 1,2,3,4,4 are painted on the 5 faces of a dice. What can the number on the sixth face be if the probability of obtaining a prime number is the same as the probability of obtaining an even number when the dice is rolled?

3) A dice is rolled together with a dice whose 5 faces have numbers 1,1,1,3,3. Write down a possible number on the sixth face of the second dice if the probability of obtaining a sum bigger than the product is more than 0.5.

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    Lv 6
    1 十年前
    最愛解答

    1)

    let t in minutes

    t=0 t=7 t=20 t=27 t=40

    ||----------||-----------------------||----------||-----------------------||

    F left C left F left C left F left

    the bus he will take if he arrive at this interval

    (refer to the time line)

    C F C F

    ||----------||-----------------------||----------||-----------------------||

    so required probability=7/20

    2)

    let the number be k it can be a prime number OR a even number

    P(prime)=P(even)

    (2+a)/6=(3+b)/6

    where

    a=1 if k is prime, =0 if k is not

    b=1 if k is even, =0if k is not

    since 2+a=3+b, a=1,b=0

    so k is a prime number that is not even

    so k is a prime number except 2

    3)

    let the number be k

    note that, the special dice has faces 1,1,1,3,3,k

    P(special dice showing an '1')=0.5

    let X be the number obtained after throwing the fist (normal) dice

    If an '1' is obtained from the second (special) dice,

    1+X>1*X

    Hence

    P(sum>product) is at least 0.5

    since P(sum>product given that special dice showing an '1')=0.5

    (as P(special dice showing an '1')=0.5)

    Also notice that the first dice has an "1" and the second dice has "3,3,k"

    1+3>1*3 and 1+k>1*k

    adding these favourable out comes,

    P(sum>product) must always >0.5

    so you can put any number

    see my summary

    for the green box(that is the number k)

    if k=1, P(sum>product)=26/36

    if k>1, P(sum>product)=21/36

    圖片參考:http://i256.photobucket.com/albums/hh182/zilu_phot...

    圖片參考:http://i256.photobucket.com/albums/hh182/zilu_phot...

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