# Video: Pack 4 • Paper 3 • Question 8

Pack 4 • Paper 3 • Question 8

02:58

### 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.