### Video Transcript

Claire took a random selection of
playing cards and put them in a box. She will take a card at random from
the box. The table shows the probabilities
of getting a heart or a diamond or a spade. The probability of selecting a
heart is 0.28, the probability of selecting a diamond is 0.04, and the probability
of selecting a spade is 0.56. Part a) What is the probability
that the card is a club? Part b) What is the least number of
cards in the box? Justify your answer.

In order to answer the first part
of the question, we will use the fact that all probabilities must add up to one or
100 percent. In this case, 0.28 plus 0.04 plus
the probability of selecting a club plus 0.56 must equal one. This means that we can subtract the
other three probabilities from one to calculate the probability of selecting a
club.

0.28 plus 0.04 plus 0.56 is equal
to 0.88. Therefore, the probability of
selecting a club is one minus 0.88. This is equal to 0.12 we can check
this by adding the four probabilities now in the table and ensuring that they add up
to one.

The second part of our question
asked us to work out the least number of cards that are in the box. In order to do this, we’ll consider
the ratio of the four suits based on their probabilities. The ratio of the suits, hearts to
diamonds to clubs to spades, is 28 to four to 12 to 56.

We can simplify this ratio by
looking for a whole number that divides exactly into all four numbers. In this case, we can divide by
four. 28 divided by four is seven, four
divided by four is one, 12 divided by four is equal to three, and 56 divided by four
is equal to 14.

The total of these ratios is
25. This means that the least number of
cards is 25 as they must be at least one of each suit — in this case, at least one
diamond as diamond had the smallest probability.

If there are 25 cards in the box,
there will be seven hearts, one diamond, three clubs, and 14 spades, based on the
original probabilities in the table.