Question

# Two dice are thrown. Let E be the event that the sum of the dice is odd, let F be the event that the first die lands on 1, and let G be the event that the sum is 5. Describe the events $EF, E \cup F, FG, EF^c , EFG.$

Solution

Verified

Event E consists of:

$\\\left\{ \left( 1,2\right), \left(1,4 \right),\left( 1,6\right) , \left(3,2 \right), \left( 3,4\right), \left( 3,6\right), \left( 5,2\right), \left(5,4 \right), \left( 5,6\right),\right.$

$\\ \left. \left(2,1\right), \left(4,1 \right),\left( 6,1\right) , \left(2,3 \right), \left( 4,3\right), \left( 6,3\right), \left( 2,5\right), \left(4,5 \right), \left( 6,5\right) \right\} \\$

Event F consists of: $\\\left\{ (1,1), (1,2), (1,3),(1,4), (1,5), (1,6) \right\} \\$Event G consists of:$\left{(1,4),(4,1),(2,3),(3,2) \right} Then\ EF = \left{ (1,2),(1,4),(1,6)\right} E\cup F = \left{ (1,1)\left( 1,2\right), (1,3) \left(1,4 \right), (1,5)\left( 1,6\right) ,\right.\left. \left(3,2 \right), \left( 3,4\right), \left( 3,6\right), \left( 5,2\right), \left(5,4 \right), \left( 5,6\right) ,\right.\left. \left(2,1\right), \left(4,1 \right),\left( 6,1\right) , \left(2,3 \right), \left( 4,3\right), \left( 6,3\right), \left( 2,5\right), \left(4,5 \right), \left( 6,5\right) \right} FG = \left{(1,4) \right} EF^{c} = \left{ \left(3,2 \right), \left( 3,4\right), \left( 3,6\right), \left( 5,2\right), \left(5,4 \right), \left( 5,6\right),\right.\left. \left(2,1\right), \left(4,1 \right),\left( 6,1\right) , \left(2,3 \right), \left( 4,3\right), \left( 6,3\right), \left( 2,5\right), \left(4,5 \right), \left( 6,5\right) \right} EFG = \left{(1,4) \right}$

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