Question bank: Probability of Complementary Events

João has a collection of 12 cards with different characters. Among them, exactly 5 are rare cards. If he randomly selects a card from the collection, what is the probability that he chooses a card that is not rare? And what is the probability of him choosing a rare card?

In a short-distance competition, an athlete has a 75% chance of winning the gold medal, 20% chance of winning the silver medal, and 5% chance of winning the bronze medal. What is the probability of the athlete winning gold or silver, but not bronze?

Joana and Pedro are competing in a coin tossing tournament. They have a normal coin and another one that has heads on both sides. First, Joana chooses one of the coins without looking and makes two tosses, noting the sequence of the faces (heads or tails). Then, Pedro tries to guess which coin Joana used, based on the noted sequence. Consider the following items: a) Calculate the probability of Joana getting 'heads-heads' with the normal coin and the two-headed coin. b) If Joana got 'heads-heads', what is the probability of Pedro guessing which coin she used? c) In general, what is the probability of Pedro guessing the coin used by Joana, regardless of the noted sequence.

In a board game, a player rolls three dice. Each die has six faces numbered from 1 to 6. The player wins the game if they get at least one 6 among the three dice rolled. Determine the probability of the player winning the game. Then, calculate the probability of the player losing the game, that is, the probability of none of the dice showing the number 6. To solve this question, you can apply the concept of complementary events, where the probability of an event A plus the probability of its complementary event A' is equal to 1.