Video Transcript
A card is drawn from a deck of
cards numbered from one to 37. What is the probability that the
number on the card is even?
We can assume that the card is
drawn at random, and therefore every card has an equal chance of being chosen. When all outcomes of an experiment
are equally likely, we can calculate the probability of a particular event occurring
by dividing the number of successful outcomes by the total number of outcomes. Here, the event we’re interested in
is that the number on the card is even. The successful outcomes are
therefore all the even-numbered cards in the deck. The total number of outcomes is the
total number of cards, which is 37. To calculate the required
probability, we first need to work out how many of the cards have even numbers on
them.
Suppose we just had the numbers one
to 36 in the deck. Because odd and even numbers
alternate, exactly half of the cards will have odd numbers, and half will have even
numbers. Half of 36 is 18, so there are 18
even-numbered cards in the deck. Adding the 37th card back in makes
no difference to the number of even cards in the deck because 37 is an odd
number. Dividing the number of even cards
by the total number of cards, we find that the probability that the number on the
card is even is 18 over 37. This fraction can’t be simplified
any further because 18 and 37 have no common factors other than one.
