54) Two persons each makes a single throw with a pair of dice, The probability that the throws are - Maths - Probability - I

Question

54) Two persons each makes a single throw with a pair of dice, The
probability that the throws are unequal given by
( a )   1 6 3 ( b )   73 6 3 ( c )   51 6 3 ( d )
  n o n e   o f   t h e s e

Anuradha Sharma · Accepted Answer

Hi,

P(scores unequal) = 1 - P(equal) = 1 - P(both total 2 or both total
3 or or both total 12)

P(both total 2) = P(1st totals 2)*P(2nd total 2) = (1/36)*(1/36) =
1/1296

P(both total 3) = P(1st totals 3)*P(2nd totals 3) = (2/36)*(2/36) =
4/1296

In a similar way the probability that both total 4, 5, 6, 7, 8, 9,
10, 11, 12 are

9, 16, 25, 35, 25, 16, 9, 4, 1 each over 1296

P(scores equal) = (1 + 4 + 9 + 16 + 25 + 36 + 25 + 16 + 9 + 4 +
1)/1296

= 146/1296 = 73/648

P(scores unequal) = 1 - 73/648 = 575/648
Regards

54) Two persons each makes a single throw with a pair of dice, The probability that the throws are unequal given by. ( a ) 1 6 3 ( b ) 73 6 3 ( c ) 51 6 3 ( d ) n o n e o f t h e s e

54) Two persons each makes a single throw with a pair of dice, The probability that the throws are unequal given by.
$(a) \frac{1}{6^{3}} (b) \frac{73}{6^{3}} (c) \frac{51}{6^{3}} (d) n o n e o f t h e s e$