Question

If two fair dice are rolled, find the probability that the sum of the dice is 10, given that the sum is greater than 4. The probability is (Simplify your answer. Type an integer or a simplified fraction.)

Answer 1

sum of dice	2	3	4	5	6	7	8	9	10	11	12
Probability	$\small \frac{1}{36}$	$\small \frac{2}{36}$	$\small \frac{3}{36}$	$\small \frac{4}{36}$	$\small \frac{5}{36}$	$\small \frac{6}{36}$	$\small \frac{5}{36}$	$\small \frac{4}{36}$	$\small \frac{3}{36}$	$\small \frac{2}{36}$	$\small \frac{1}{36}$

The probability that sum of the dice is 10 and the sum is greater than 4 is $\small \frac{3}{36}$

The probability that the sum is greater than 4 is $\small \frac{30}{36}$

The probability that the sum of dice is 10, given that the sum greater than 4 is ( conditional probability )

$\small \frac{\frac{3}{36}}{\frac{30}{36}}=\frac{3}{30}=\frac{1}{10}=0.1$

Answer 2

SOLUTION :

Number of events having sum > 4

Sum 5 : (1, 4), (4, 1), (2, 3), (3, 2),                     : 4 events

Sum 6 : (1, 5), (5, 1), (2, 4), (4, 2), (3, 3)            : 5 events 

Sum 7 :  (1, 6), (6,1), (2, 5), (5, 2), (3, 4), (4, 3) : 6 events

Sum 8 : (2, 6). (6, 2), (3, 5), (5, 3), (4, 4)            : 5 events

Sum 9 : (3, 6), (6, 3), (4, 5), (5, 4)                      : 4 events

Sum 10 : (4, 6), (6, 4), (5, 5)                               : 3 events

Sum 11 : (5, 6), (6, 5)                                         : 2 events

Sum 12 : (6, 6)                                                    : 1 event

                                                                           __________

Total                                                                    : 30 events

                                                                           ___________ 

Events that sum = 10 :  (4, 6), (6, 4), (5, 5)        : 3 events

Events common to both cases  : (4, 6), (6, 4), (5, 5)   : 3 events

P(sum = 10 | sum > 4)

= Number of events common to both cases / Space of sum > 4

= 3 / 30

= 1/10 (ANSWER).