A school has 5 Spanish teachers and 4 French teachers. The school’s principal randomly chooses 2 of the teachers to attend a conference. What is the probability that the principal chooses 2 Spanish teachers?
You can look at it as a 9 card deck. Spanish teacher are spades, and French teachers are diamonds. So we have 5 spades and 4 diamonds in our deck. Now when the principal randomly picks 2 teachers, it’s the same as us drawing two cards from the deck; once a card is drawn, it doesn’t go back into the deck.
Thus, for our problem we are wondering what the probability is that the first two cards we draw are spades. Our first draw has a probability of 5/9 to get a spade because 5 of the 9 cards are spades.
Now before our second draw we need to remember that our deck just got smaller by one spade. So the probability of us drawing a spade for our second card is 4/8.
Now we multiply the two probabilities together to obtain our final answer: