Quiz problem on combinatorics

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This topic contains 2 replies, has 2 voices, and was last updated by  Aniruddha Bardhan 1 month ago.

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  • #30009

    Aniruddha Bardhan
    Participant

    See the attchment

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    #30549

    Camellia Ray
    Participant

    N/10= 1-N/10 at N =5; so when the frog is aat lily pad 5 it has equal probability of either being eaten up by the snake or get escaped. Let (P_k) represents the probability that the frog escapes if it is currently on pad k then (P_5)= 1/2.

    Solving the following equations

    (P_1)= 9/10 (P_2)

    (P_2)= 2/10 (P_1)+8/10 (P_3)

    (P_3)= 3/10(P_2)+ 7/10 (P_4)

    (P_4)= 4/10 (P_3)+6/10 (P_5)

    (P_5)= 1/2

    SOLVING THE ABOVE EQUATIONS STEP BY STEP WE GET

    \(P_4\)= 2/5 \(P_3\)+ 3/10

    (P_3)= 3/10 (P_2) +7/10 ×(2/5 (P_3 +3/10))

    (P_3)= 3/10 (P_2) + 14/50 (P_3) +21/100

    36/50 (P_3)= 3/10 (P_2) + 21/100

    \P_3)= (3/10 (P_2) +21/100)×50/36

    (P_2)= 2/10 (P_1) + 8/10 ( 3/10 (P_2) +21/100)×50/36

    = 2/10 (P_1) +1/3 (P_2) + 7/30

    2/3 (P_2)=2/10 (P_1)+7/30

    (P_2) = 3/10 (P_1) + 7/20

    (P_1) = 9/10×(3/10 (P_1) + 7/20)

    (P_1)= 27/100 (P_1) +63/200

    (P_1)×73/100= 63/200

    (P_1)= 63/146

     

     

     

     

     

     

     

     

    #30602

    Aniruddha Bardhan
    Participant

    Thanks maam.

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