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.
