P(5 or 8) = [tex]\frac{2}{12}[/tex] = [tex]\frac{1}{6}[/tex] or 16.666%.
Step-by-step explanation:
Step 1; To determine the chances of a particular event to occur, we divide the number of outcomes that are favorable by the number of possible outcomes. In this case, the favorable outcomes are those which have both 5 and 8 in their 2 digit number and the number of outcomes is a count of all the ways in which the four numbers 6, 5, 1 and 8 can be used to form any two-digit numbers.
Step 2; From the tree diagram, we infer that there are two numbers that can be formed with both 5 and 8 i.e. 58 and 85. The total number of possible outcomes is 12 i.e. 65, 61, 68, 56, 56, 58, 16, 15, 18, 86, 85 and 81.
So P(5 or 8) = [tex]\frac{numberof favorableoutcomes}{total number of outcomes}[/tex] = [tex]\frac{2}{12}[/tex] = [tex]\frac{1}{6}[/tex] = 0.1666 × 100 = 16.66%.
