Question

A die is rolled. Find the probability of the given event. Write your answers as whole numbers or reduced fractions.
(a) The number showing is a 4
P(4) = (b) The number showing is an even number
P(even) =
(c) The number showing is greater than 3
P(greater than 3) =

Answer 1

The probability for given conditions are a) p(4)=0.166, b) p(even)=0.5 and c) p(greater than 3)=0.5

A die is rolled, then the sample space for outcomes is {1,2,3,4,5,6}

Total number of outcomes =6

1. Probability of showing number 4.                                                                   number of favourable outcomes is 1 because there is only one 4 in the sample space of outcomes ,                           $P(4)=\frac{number\ of\ favourable\ outcomes}{total\ number\ of\ outcomes}\\\\P(4)=\frac{1}{6}=0.166$
2. Probability of showing an even number,                                                        even numbers in sample space are {2,4,6}                                                        number of favourable outcomes =3                                                                      $P(even)=\frac{3}{6}=\frac{1}{2}=0.5$
3. Probability of showing a number greater than 3,                                                 numbers greater then three is sample space are {4,5,6}                                    number of favourable outcomes =3                                                                          $P(greater\ than\ 3)=\frac{3}{6}=\frac{1}{2}=0.5$

Thus, the probability for given conditions are a)p(4)=0.166, b)p(even)=0.5 and c)p(greater than 3)=0.5

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