We are told that a class is debating on what gift to send to an exchange student in Italy. Out of 32 students, 10 chose a card, 12 chose a T-shirt, 6 chose a video game, and 4 chose a bracelet. We are asked to find the probability that a randomly selected present is a card or a bracelet.
P(card or bracelet)=?
Since each student can pick only one gift, the events of choosing different gifts are mutually exclusive. Let's recall the formula for the probability of mutually exclusive events.
If two events A and B are mutually exclusive, the probability that A or B occurs can be calculated using the following equation.
P(AorB)=P(A)+P(B)
Using this formula, we can write the following equation.
P(card or bracelet)=P(card)+P(bracelet)
Next, let's calculate P(card) and P(bracelet). We can start with P(card), which is the probability that a randomly chosen present is a card. We know that 10 out of 32 students want to send a card to the exchange student.
P(card)=10/32
Now, let's calculate P(bracelet). We know that 4 out of 32 students want to send a bracelet.
P(bracelet)=4/32
Finally, we can calculate the probability that a randomly selected gift is a card or a bracelet.
