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Probability

Question
CBSEENMA12033871

A pair of dice is thrown 6 times. If getting a total of 9 is considered a success, what is the probability of at least 5 successes?

Solution

A pair of dice is thrown. Therefore various outcomes are

11

12

13

14

15

16

21

22

23

24

25

26

31

32

33

34

35

36

41

42

43

44

45

46

51

52

53

54

55

56

61

62

63

64

65

66

 ∴ total number of outcomes = 36
Favorable outcomes are 36, 45, 54 and 63.
∴ number of favorable outcomes = 4
therefore space space space space straight p space equals space 4 over 36 minus 1 over 9 comma space space space straight q space equals space 1 space minus space straight q space equals space 1 space minus space 1 over 9 space equals space 8 over 9
Also space straight n space equals space 6
straight P left parenthesis at space least space 5 space successes right parenthesis space equals space straight P left parenthesis 5 right parenthesis space plus space straight P left parenthesis 6 right parenthesis
space space space space space space space space space space space space space space space space equals space straight C presuperscript 6 subscript 5 open parentheses 8 over 9 close parentheses to the power of 6 minus 5 end exponent space open parentheses 1 over 9 close parentheses to the power of 5 plus straight C presuperscript 6 subscript 6 space open parentheses 8 over 9 close parentheses to the power of 6 minus 6 end exponent space open parentheses 1 over 9 close parentheses to the power of 6
space space space space space space space space space space space space space space space space equals space straight C presuperscript 6 subscript 1 space open parentheses 8 over 9 close parentheses to the power of 1 space open parentheses 1 over 9 close parentheses to the power of 5 space plus space straight C presuperscript 6 subscript 0 space open parentheses 8 over 9 close parentheses to the power of 0 space open parentheses 1 over 9 close parentheses to the power of 6
space space space space space space space space space equals space 6 over 1 cross times 8 over 9 cross times 1 over 9 to the power of 5 plus 1 space cross times space 1 space cross times space 1 over 9 to the power of 6 space equals 1 over 9 to the power of 6 left parenthesis 48 plus 1 right parenthesis space equals space 49 over 531441
          

 

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