Question

Julie wants to randomly choose two out of three friends, Margarite, Anita, and Sasha, to go with her to a concert. In which method does one of Julie's friends have more than a fair chance of being chosen?

a. Julie rolls a number cube. If the number is 1 or 2. then Sasha does not go. If the number is 3 or 4, Margarite does not go. If the number is 5 or 6. Anita does not go.
b. Julie flips three coins, one for each friend. If exactly two coins match, then the two corresponding friends go. Otherwise, she continues to flip the three coins until exactly two coins match.
c. Julie has 5 slips of paper numbered 1 to 5. Each friend draws a slip at random, and the friends with the highest and lowest numbers go.
d. Julie flips a coin. If it's tails, Margarite and Anita will go the concert. If it's heads, then Sasha will go to the concert. Julie will then flip a coin to choose between Margarite and Anita.

Answer 1

Option d is the method in which Julie's friend Sasha has less than a fair chance of being chosen for the concert, thereby giving Margarite and Anita more than a fair chance.

Step-by-step explanation:

Julie wants to randomly choose two out of three friends to go with her to a concert, but she wants to do it fairly. To determine which method gives one friend more than a fair chance, we can analyze each option:

• Option a: Rolls a number cube. This method is fair as each friend has a 2 in 6 chance of not going, which means each friend has a 4 in 6, or 2 in 3 chance of going.
• Option b: Flips three coins. This method is also fair because it doesn't stop until exactly two coins match, which gives each friend an equal chance of going with every attempt.
• Option c: Draws slips of paper numbered 1 to 5. This method seems fair at first, but because there are 5 slips for 3 people, it is not perfectly balanced and could give someone a slight advantage or disadvantage, depending on the slip distribution.
• Option d: Flips a coin twice. This method is unfair to Sasha because she can only be chosen if the first coin is heads. Margarite and Anita, however, have two chances: if the first coin is tails or if the first is heads and the second flip selects them.

Therefore, option d gives one of Julie's friends (Sasha) less than a fair chance, and conversely, it increases the chances for Margarite and Anita.