search(["12"])For problem 12 on page 14, the task is to create and solve a probability problem involving mutually exclusive events.

Mutually exclusive events are events that cannot occur at the same time. An example of such events could be drawing a card from a deck where you are asked to find the probability of drawing either a heart or a club, two mutually exclusive events.

Let’s create a probability problem:

• A deck of cards has 52 cards.
• You are asked to find the probability of drawing either a red card or a black card.

Since red cards (hearts and diamonds) and black cards (clubs and spades) are mutually exclusive events (you can't draw a card that is both red and black), you can simply add the probabilities of drawing a red card and a black card.

There are 26 red cards and 26 black cards, so the total number of favorable outcomes is:

• Probability of drawing a red card: $P(\text{Red}) = \frac{26}{52} = \frac{1}{2}$
• Probability of drawing a black card: $P(\text{Black}) = \frac{26}{52} = \frac{1}{2}$

Thus, the total probability of drawing either a red or a black card is: $P(\text{Red or Black}) = P(\text{Red}) + P(\text{Black}) = \frac{1}{2} + \frac{1}{2} = 1$

This is a simple case because the total probability is 1, as the event covers the entire deck.

Would you like more examples or further details on this topic?