Question

You roll two fair dice, one green and one red. (a) Are the outcomes on the dice independent? Yes No (b) Find P(1 on green die and 5 on red die). (Enter your answer as a fraction.) (c) Find P(5 on green die and 1 on red die). (Enter your answer as a fraction.) (d) Find P((1 on green die and 5 on red die) or (5 on green die and 1 on red die)). (Enter your answer as a fraction.)

Answer 1

Answer:

a

  Yes

b

 $P(1 \& 5) = \frac{1}{36}$

c

 $P(5 \& 1) = \frac{1}{36}$

d

 $P(5 \& 1 | 1\& 5 ) = \frac{1}{18}$

Step-by-step explanation:

From the question we are told that

     Two fair dice, one green and one red were rolled

Generally the  outcomes on the dice independent because the outcome on the first dice is not affected by the second die

Generally the  probability of getting a 1  on a dice rolled is  $P(1) = \frac{1}{6}$

the  probability of getting a 5 on a dice rolled is  $P(5) = \frac{1}{6}$

Generally the probability of P(1 on green die and 5 on red die) is mathematically represented as

         $P(1 \& 5) = \frac{1}{6} *\frac{1}{6}$

         $P(1 \& 5) = \frac{1}{36}$

Generally the probability of P(5 on green die and 1 on red die) is mathematically represented as

          $P(5 \& 1) = \frac{1}{6} *\frac{1}{6}$

         $P(5 \& 1) = \frac{1}{36}$

Generally the probability of P((1 on green die and 5 on red die) or (5 on green die and 1 on red die)) is mathematically represented as

          $P(5 \& 1 | 1\& 5 ) = \frac{1}{36} + \frac{1}{36}$

         $P(5 \& 1 | 1\& 5 ) = \frac{1}{18}$