Question bank: Probability of Complementary Events

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Question 1:

Hard

When tossing a fair coin, we have the same probability of getting heads or tails, that is, 0.5 or 50%. If we toss two coins, the probability of getting at least one head is 75% (or three out of four possibilities: HH, HT, TH). Considering this situation, analyze the tossing of three coins in sequence and calculate the probability of getting at least one head. Then, determine the probability that when tossing three coins, none of them will be heads. Finally, mathematically justify why the sum of the probabilities of getting at least one head and not getting a head when tossing three coins is equal to 1.

Probability of Complementary Events

Theorical Question

Contextualized Question

Question 2:

Medium

When tossing 4 coins in the air, what is the probability of getting at least one head?

Probability of Complementary Events

Basic Calculus

Question 3:

Medium

Joana likes to collect marbles of different colors. In the box where she keeps her marbles, she has: 4 red, 3 blue, 2 green, and 1 yellow. Joana will randomly pick a marble with her eyes closed. What is the probability of Joana picking a marble that is neither green nor yellow?

Probability of Complementary Events

Question 4:

Very Hard

An urn contains 3 red balls and 2 blue balls. A player draws a ball from the urn, observes its color, and puts it back in the urn. Then, they draw another ball and repeat the observation and replacement procedure. After that, the player draws a third ball and does not put it back in the urn. Considering that the color of each drawn ball is independent of the colors of the other balls and that the balls, after being replaced, are distributed equally in the urn, calculate the probability that the first ball drawn is red, the second ball is blue, and the third ball is also blue.

Probability of Complementary Events

Theorical Question

Contextualized Question

Question 5:

Hard

Eighth-grade class is conducting a science project involving understanding probability. In one of the experiments, they toss three fair coins and record the results. Each coin can land on 'heads' (H) or 'tails' (T). The students must calculate the probability of at least one coin showing tails. To complete this task, they must understand the concept of complementary events: the probability of an event A occurring is 1 minus the probability of A not occurring. Additionally, they know that in a coin-tossing experiment, the sum of all possible probabilities must be 1. Based on this scenario, describe how the students can calculate the probability of at least one coin showing tails and explain the concept of complementary events applied to this calculation.

Probability of Complementary Events

Multidisciplinary Question

IARA TIP

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