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There are four classmates. Ana, Beta, Ceta and Deta. During the break all of them tiffed (probability is p) or became best friends (probability is 1-p). And all with each other tiffed or became best friend. After lessons, girls telling interesting stories or rumors for their best friends. Suppose that Ana to know something interesting. And we need to calculate probability that Deta will hear this news.

I dont know how to calculate this in the simply way. I just wrote all options. Results of all this is:(plus mean that became friends, minus - that became enemies)

1)A+B, A+C, A+D, B+C, B+D, C+D

2)A-B, A+C, A+D, B+C, B+D, C+D

3)A+B, A-C, A+D, B+C, B+D, C+D

4)A+B, A+C, A-D, B+C, B+D, C+D

5)A+B, A+C, A+D, B-C, B+D, C+D

6)A+B, A+C, A+D, B+C, B-D, C+D

7)A+B, A+C, A+D, B+C, B+D, C-D

8)A-B, A-C, A+D, B+C, B+D, C+D

9*)A-B, A+C, A+D, B-C, B+D, C-D

10)A-B, A+C, A-D, B+C, B+D, C+D

11)A-B, A+C, A+D, B-C, B+D, C+D

12)A-B, A+C, A+D, B+C, B-D, C+D

13)A-B, A+C, A+D, B+C, B+D, C-D

14)A+B, A-C, A-D, B+C, B+D, C+D

15)A+B, A-C, A+D, B-C, B+D, C+D

16)A+B, A-C, A+D, B+C, B-D, C+D

17)A+B, A-C, A+D, B+C, B+D, C-D

18)A+B, A+C, A-D, B-C, B+D, C+D

19)A+B, A+C, A-D, B+C, B-D, C+D

20)A+B, A+C, A-D, B+C, B+D, C-D

21)A+B, A+C, A+D, B-C, B-D, C+D

22)A+B, A-C, A+D, B+C, B-D, C-D

23)A-B, A-C, A-D, B+C, B+D, C+D

24)A-B, A-C, A+D, B-C, B+D, C+D

25)A-B, A-C, A+D, B+C, B-D, C+D

26)A-B, A-C, A+D, B+C, B+D, C-D

27)A-B, A+C, A-D, B-C, B+D, C+D

28)A-B, A+C, A-D, B+C, B-D, C+D

29)A-B, A+C, A-D, B+C, B+D, C-D

30)A-B, A+C, A+D, B-C, B-D, C+D

31)A-B, A+C, A+D, B-C, B+D, C-D

32)A-B, A+C, A+D, B+C, B-D, C-D

33)A+B, A-C, A-D, B-C, B+D, C+D

34)A+B, A-C, A-D, B+C, B-D, C+D

35)A+B, A-C, A-D, B+C, B+D, C-D

36)A+B, A-C, A+D, B-C, B-D, C+D

37)A+B, A-C, A+D, B-C, B+D, C-D

38)A+B, A-C, A+D, B+C, B-D, C-D

39)A+B, A+C, A-D, B-C, B-D, C+D

40)A+B, A+C, A-D, B-C, B+D, C-D

41)A+B, A+C, A-D, B+C, B-D, C-D

42)A+B, A+C, A+D, B-C, B-D, C-D

43)A+B, A+C, A-D, B-C, B-D, C-D

44*)A+B, A-C, A-D, B+C, B-D, C+D

45)A+B, A-C, A+D, B-C, B-D, C-D

46)A+B, A-C, A-D, B+C, B-D, C-D

47)A+B, A-C, A-D, B-C, B+D, C-D

48)A+B, A-C, A-D, B-C, B-D, C+D

49)A-B, A+C, A+D, B-C, B-D, C-D

50)A-B, A+C, A-D, B+C, B-D, C-D

51)A-B, A+C, A-D, B-C, B+D, C-D

52)A-B, A+C, A-D, B-C, B-D, C+D

53)A-B, A-C, A+D, B+C, B-D, C-D

54)A-B, A-C, A+D, B-C, B+D, C-D

55)A-B, A-C, A+D, B-C, B-D, C+D

56)A-B, A-C, A-D, B+C, B+D, C-D

57)A-B, A+C, A-D, B-C, B+D, C+D

58)A+B, A-C, A-D, B-C, B-D, C-D

59)A-B, A+C, A-D, B-C, B-D, C-D

60)A-B, A-C, A+D, B-C, B-D, C-D

61)A-B, A-C, A-D, B+C, B-D, C-D

62)A-B, A-C, A-D, B-C, B+D, C-D

63)A-B, A-C, A-D, B-C, B-D, C+D

64)A-B, A-C, A-D, B-C, B-D, C-D

So I calculated that 48 of these statisfies that Deta will get rumors. And inserted probabilistic values and sumed polynomials got that probability is equal to -2p^6+5p^5-2p^4-2p^3+1.

I dont realy know or this answer is correct. When p is 0.5, looks like good if my calculations that 48 variants statisfy with condition.

I want to ask you help. Maybe there is easier way to solve this task? Thanks.