Use the addition rule to find the probability of the following event: Obtaining a sum of 6 or doubles (same number on each die) when a pair of dice is rolled once. Express your answer as a decimal rounded to 1 decimal place.

Solution

U se t h e a dd i t i o n r u l e t o f in d t h e p ro babi l i t y o f t h e f o ll o w in g e v e n t : O b t ainin g a s u m o f 6 or d o u b l es (s am e n u mb er o n e a c h d i e) w h e n a p ai r o f d i ce i s ro ll e d o n ce . E x p ress yo u r an s w er a s a d ec ima l ro u n d e d t o 1 d ec ima l pl a ce .

Solution

\frac{5}{18}

Decimal

0.27777 \dots

Solution steps

Find the probability of the following event : Obtaining a sum of 6:

\frac{5}{36}

Find the probability of the sum doubles ( same number on each die ) when a pair of dice is rolled once:

\frac{1}{6}

Find the probability of the following event : Obtaining a sum of 6 and the sum doubles ( same number on each die ) when a pair of dice is rolled once:

\frac{1}{36}

Use the Inclusion-Exclusion formula

P (X \lor Y) = P (X) + P (Y) - P (X \land Y)

= \frac{5}{36} + \frac{1}{6} - \frac{1}{36}

\frac{5}{36} + \frac{1}{6} - \frac{1}{36} = \frac{5}{18}

= \frac{5}{18}

Popular Examples

A certain loan program offers an interest rate of 4% compounded continuously. Assuming no payments are made, how much would be owed after seven years on a loan of \$1900 A card from a standard deck is chosen at random, then a coin is tossed. What is the probability of getting an ace and tails?Felix has 5,483 in an account. The interest rate is 12% compounded annually.To the nearest cent, how much interest will he earn in 2 years?0.175% of what number is 69.3 The area of a circle is 100pi square meters. What is the radius?