Question Video: Identifying Scenarios Representing Independent Events Mathematics

In which of the following scenarios are A and B independent events? [A] A die is rolled. Event A is rolling an even number, and event B is rolling a prime number. [B] A die is rolled, and a coin is flipped. Event A is rolling a six on the die, and event B is the coin landing on heads. [C] A student leaves their house on the way to school. Event A is them arriving at the bus stop in time to catch the bus, and event B is them getting to school on time. [D] A child takes two candies at random from a bag which contains chewy candies and crunchy candies. Event A is them taking a chewy candy first, and event B is them taking a crunchy candy second. [E] A teacher selects two students at random from a group of five boys and five girls. Event A is the teacher selecting a boy first, and event B is the teacher selecting a girl second.

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Video Transcript

In which of the following scenarios are A and B independent events? Option (A) a die is rolled. Event A is rolling an even number, and event B is rolling a prime number. Option (B) a die is rolled, and a coin is flipped. Event A is rolling a six on the die, and event B is the coin landing on heads. Option (C) a student leaves their house on the way to school. Event A is them arriving at the bus stop in time to catch the bus, and event B is them getting to school on time. Option (D) a child takes two candies at random from a bag which contains chewy candies and crunchy candies. Event A is them taking a chewy candy first, and event B is them taking a crunchy candy second. Option (E) a teacher selects two students at random from a group of five boys and five girls. Event A is the teacher selecting a boy first, and event B is the teacher selecting a girl second.

We recall the two events are independent if the outcome of one does not affect the outcome of the other. Let’s look at all five of our options in order. In option (A), we are rolling a die. Event A is rolling an even number. And event B, rolling a prime number. These events would be independent if there were no even numbers that are also prime numbers. We know that a regular die is numbered one to six. The even numbers are therefore two, four, and six. Prime numbers are the numbers with exactly two factors. This means that on the die, we have two, three, and five. As the number two is an even number and a prime number, event A and event B are not independent. This means that option (A) is not the correct answer.

Option (B) involves rolling a die and flipping a coin. Event A is rolling a six on the die, and event B is the coin landing on heads. Rolling the die has no impact on flipping the coin, and vice versa. This means that the outcome of event A does not affect the outcome of event B. Event A and B are therefore independent, and this is a correct answer. Let’s look at our three other options to see if any of these are also independent.

In option (C), event A is arriving at the bus stop in time to catch the bus. And event B is getting to school on time. If a student misses the bus as they don’t arrive at the bus stop in time, then their probability or chance of getting to school on time will be affected. This means that the outcome of event A does affect the outcome of event B. In this scenario, A and B are not independent.

In option (D), a child is selecting two candies from a bag. Event A is taking a chewy candy first. And event B, taking a crunchy candy second. After the first candy is removed, there will be one less candy in the bag. This means that the outcome of the first candy will affect the outcome of the second candy. Taking a chewy candy first and a crunchy candy second are not independent. This is because event B is affected by event A.

Option (E) is a similar scenario to option (D). This time a teacher is selecting two students: event A being selecting a boy first, and event B, selecting a girl second. We are told there are five boys and five girls. Selecting a boy first will reduce the number of boys to four. This will, in turn, have an impact on the chance or probability of selecting a girl second. Once again, event A does affect event B. Therefore, the events are not independent. The only one of our five scenarios with independent events is option (B). Rolling a six on a die and flipping a head on a coin are independent events.

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