A game consists of 5 cups turned upside down, under one of the cups is a prize. 5 friend's pick a cup in turn and lifts it up, if they get the prize, they win , but if not, the cup is removed and the next friend picks. What position is it best to pick?

The first friend to choose has 5 cups to pick from and only 1 that will win them the prize, so their probability of winning is 1/5.The 2nd friend relies on the first friend to not win, this with a probability of 4/5, and also for them to pick the winning cup, a probability of 1/4. As both of these events have to occur we need to multiply the probabilities to get 4/5 x 1/4 = 1/5.Similarly for the 3rd player, they require both 2 previous players to 'lose' and them to win, with probability 4/5 x 3/4 x 2/3 = 1/5This argument applies for both other players.Therefore, all friends have probability 1/5 of winning the prize, and therefore it does not matter what position you pick a cup in.Extensions: What if there are n friends and n cups? What is there are 5cups, 5 friends but now 2 prizes?

Answered by Alex M. Maths tutor

2022 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

Solve algebraically the simultaneous equations: 6x=5-2y 12.5=3x+3y


How do you solve the equation '2x + 1 = 5'?


The perimeter of a right-angled triangle is 81 cm. The lengths of its sides are in the ratio 2 : 3 : 4. Work out the area of the triangle.


(6x+4)/(2x- 2) + 3 = 4 solve for x


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences