Two fair dice are thrown together two times. Find the probability of obtaining a sum of seven in the first throw and a sum of four in the second throw.

Two fair dice are thrown together two times. Find the probability of obtaining a sum of seven in the first throw and a sum of four in the second throw. 

Answer Details

P(a sum of 7)

= 636 $\frac{\mathrm{<span\; style="font-size:\; 16px;\; font-family:\; Ubuntu;">6</span>}}{\mathrm{<span\; style="font-size:\; 16px;\; font-family:\; Ubuntu;">36</span>}}$ 

and P(a sum of 4)

= 336    $\frac{\mathrm{<span\; style="font-size:\; 16px;"> 3</span>}}{\mathrm{<span\; style="font-size:\; 16px;">36</span>}}$

P(a sum of 4)

= 336 $\frac{3}{36}$ 

P(a sum of 7 and a sum of 4)

= 636×336 $\frac{6}{36}\times \frac{3}{36}$ = 172 $\frac{1}{72}$