Diners choose one starter and one main from the options given in the table below - OCR - GCSE Maths - Question 8 - 2017 - Paper 1

To calculate the fraction of meal combinations that include at least one vegetarian option, we first find the total number of combinations:

• Total starters: 3 (Cheese salad, Prawn cocktail, Mozzarella sticks)
• Total mains: 4 (Steak and chips, Fish and chips, Tomato pizza, Pork chops, Nut cutlet)

Total meal combinations = Total starters × Total mains = 3 × 5 = 15.

Now, we count the combinations with at least one vegetarian option:

• Vegetarian starters: 3 (Cheese salad, Mozzarella sticks)
• Vegetarian mains: 3 (Tomato pizza, Nut cutlet)

Combinations with at least one vegetarian starter:

• Cheese salad: (Steak and chips, Fish and chips, Tomato pizza, Pork chops, Nut cutlet) = 5 combinations
• Mozzarella sticks: (Steak and chips, Fish and chips, Tomato pizza, Pork chops, Nut cutlet) = 5 combinations

Combinations with vegetarian mains:

• For Tomato pizza and Nut cutlet, we have: (Cheese salad, Prawn cocktail, Mozzarella sticks) = 3 combinations each.

Therefore:

• Total combinations with at least one vegetarian option = 5 + 5 + 3 + 3 = 16.

Calculating the fraction:

• Fraction = (Number of combinations with at least one vegetarian option) / (Total number of combinations) = 16 / 15 = 16/15 or simplified gives the fraction.