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In which of the following scenarios are A and B independent events?
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Option (A) a die is rolled.
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Event A is rolling an even number, and event B is rolling a prime number.
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Option (B) a die is rolled, and a coin is flipped.
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Event A is rolling a six on the die, and event B is the coin landing on heads.
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Option (C) a student leaves their house on the way to school.
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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.
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Option (D) a child takes two candies at random from a bag which contains chewy candies and crunchy candies.
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Event A is them taking a chewy candy first, and event B is them taking a crunchy candy second.
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Option (E) a teacher selects two students at random from a group of five boys and five girls.
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Event A is the teacher selecting a boy first, and event B is the teacher selecting a girl second.
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We recall the two events are independent if the outcome of one does not affect the outcome of the other.
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Let’s look at all five of our options in order.
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In option (A), we are rolling a die.
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Event A is rolling an even number.
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And event B, rolling a prime number.
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These events would be independent if there were no even numbers that are also prime numbers.
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We know that a regular die is numbered one to six.
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The even numbers are therefore two, four, and six.
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Prime numbers are the numbers with exactly two factors.
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This means that on the die, we have two, three, and five.
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As the number two is an even number and a prime number, event A and event B are not independent.
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This means that option (A) is not the correct answer.
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Option (B) involves rolling a die and flipping a coin.
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Event A is rolling a six on the die, and event B is the coin landing on heads.
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Rolling the die has no impact on flipping the coin, and vice versa.
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This means that the outcome of event A does not affect the outcome of event B.
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Event A and B are therefore independent, and this is a correct answer.
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Let’s look at our three other options to see if any of these are also independent.
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In option (C), event A is arriving at the bus stop in time to catch the bus.
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And event B is getting to school on time.
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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.
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This means that the outcome of event A does affect the outcome of event B.
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In this scenario, A and B are not independent.
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In option (D), a child is selecting two candies from a bag.
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Event A is taking a chewy candy first.
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And event B, taking a crunchy candy second.
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After the first candy is removed, there will be one less candy in the bag.
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This means that the outcome of the first candy will affect the outcome of the second candy.
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Taking a chewy candy first and a crunchy candy second are not independent.
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This is because event B is affected by event A.
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Option (E) is a similar scenario to option (D).
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This time a teacher is selecting two students: event A being selecting a boy first, and event B, selecting a girl second.
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We are told there are five boys and five girls.
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Selecting a boy first will reduce the number of boys to four.
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This will, in turn, have an impact on the chance or probability of selecting a girl second.
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Once again, event A does affect event B.
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Therefore, the events are not independent.
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The only one of our five scenarios with independent events is option (B).
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Rolling a six on a die and flipping a head on a coin are independent events.