Sophie is organising a raffle. - Each raffle ticket costs 50p. - She sells 400 tickets. - The probability that a ticket, chosen at random, wins a prize is 0.1. - Each winning ticket receives a prize worth £3. Sophie says I expect the raffle to make over £100 profit. Show that Sophie is wrong.

Photo AI

Sophie is organising a raffle - OCR - GCSE Maths - Question 4 - 2019 - Paper 6

Question 4

Sophie is organising a raffle. - Each raffle ticket costs 50p. - She sells 400 tickets. - The probability that a ticket, chosen at random, wins a prize is 0.1. - Ea... show full transcript

Worked Solution & Example Answer:Sophie is organising a raffle - OCR - GCSE Maths - Question 4 - 2019 - Paper 6

Step 1

Calculate Total Revenue

96%

114 rated

Answer

To find the total revenue from selling 400 tickets at 50p each, we calculate:

[ \text{Total Revenue} = 400 \times 0.5 = £200 ]

Step 2

Calculate Expected Prize Payout

99%

104 rated

Answer

The probability of a ticket winning is 0.1. Therefore, the expected number of winning tickets can be calculated as:

[ \text{Expected Winning Tickets} = 400 \times 0.1 = 40 ]

Each winning ticket receives a prize of £3, so the expected total prize payout is:

[ \text{Total Prize Payout} = 40 \times 3 = £120 ]

Step 3

Calculate Expected Profit

96%

101 rated

Answer

Finally, we calculate the expected profit by subtracting the total prize payout from the total revenue:

[ \text{Expected Profit} = \text{Total Revenue} - \text{Total Prize Payout} = 200 - 120 = £80 ]

Since £80 is not greater than £100, this shows that Sophie is wrong.

Join the GCSE students using SimpleStudy...

97% of Students

Report Improved Results

98% of Students

Recommend to friends

100,000+

Students Supported

1 Million+

Questions answered

;