Question

The spinner has 8 different rewards and the gift card is 1/8

2. Two brothers, Paco and Jose, walk up to the spinner next. They’re both hoping to win a $10 gift card.
(a) Jose spins first and wins a $10 gift card. He says to his brother, “My winning a $10 gift card just reduced the probability of your winning a $10 gift card.” Paco replies, “No way!” Who is correct? Explain.
(b) Paco spins and wins a $10 gift card. He says, “Amazing! The probability of us both winning a $10 gift card must be less than 1%!” Is Paco correct? Explain.

Answer 1

The probability of winning the gift card in the first place is always 1/8 no matter how many people have spun the gift card.  That being said, by the same principal, the change of them both winning a gift card is 2/16 which reduces to 1/8.  So the probability stays the same no matter what. If there was a limited number of gift cards, the probability would change with each spin and each win.  But it didn't say the number of cards available changes, just that it stays 1/8.