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

To determine the fraction of meal combinations with at least one vegetarian option, we first identify the possible starters and mains.

Starters:

1. Cheese salad (v)
2. Prawn cocktail
3. Mozzarella sticks (v)

Mains:

1. Steak and chips
2. Fish and chips
3. Tomato pizza (v)
4. Pork chops
5. Nut cutlet (v)

Total combinations:
There are 3 starters and 5 mains, so the total number of combinations is: $3 imes 5 = 15$

Combinations with at least one vegetarian option:

• For each starter, we check possible mains:
  • Cheese salad (v): {Steak, Fish, Tomato, Pork, Nut} = 5 combinations
  • Prawn cocktail: {Steak, Fish, Tomato, Pork, Nut} = 5 combinations
  • Mozzarella sticks (v): {Steak, Fish, Tomato, Pork, Nut} = 5 combinations
  • Totals with at least one vegetarian option are:
  1. Cheese salad (v) with any main (5)
  2. Mozzarella sticks (v) with any main (5)
  3. Prawn B with packs of only vegetarian mains - Tomato Pizza (v), Nut Cutlet (v) counting for the mains with 2 vegetarian choices.

Thus, we have: $5 + 5 + 2 = 12$ combinations with at least one vegetarian option.

Fraction of combinations with at least one vegetarian option: $\frac{12}{15} = \frac{4}{5}$