a The available menus is the number of combinations in the sample space. By multiplying the number of dishes in the horizontal direction by the number of desserts in the vertical direction, we get the total number of menus.
b Choosing both at random is the same as writing down all twelve of the possibilities and putting them into a hat before drawing one. This gives each complete meal the same probability to be chosen from the hat.
P(Specific Meal)= 112
If each complete meal has the same probability of being chosen, then each menu is equally likely.
c To determine the probability of picking a menu without meat and the probability of picking a meal with chocolate, we will mark these combinations in two separate sample spaces.
From the diagram, we see that there are 6 menus that do not include meat. Also, 8 menus contain chocolate. Therefore, the favorable outcomes are 6 and 8 respectively. From Part A, we know that the total of possible outcomes is 12. With this, we can determine the probability for each event.
P(no meat)&=6/12=1/2 [0.8em]
P(chocolate)&=8/12=2/3
