Question

Ingrid and Thomas both enter a raffle where they get a chance to pull one winning ticket from a box. If there are 25 tickets in the box and tickets are not replaced, what is the probability that both will pull a losing ticket from the box? Write your answer as a simplified fraction.

Answer 1

In a bag with plastic shapes, there are 6 triangles, 4 circles, and 5 squares. What is the probability of pulling out two triangles if the first shape is replaced before the second shape is pulled out? Write your answer as a simplified fraction.

Answer 2

How many outcomes are in the sample space of rolling two number cubes labeled 1–6? Use the method of your choice.

Answer 3

Since the tickets are not replaced, after Ingrid pulls out a ticket, there will be 24 tickets left in the box. The probability that Ingrid pulls out a losing ticket is $\frac{24}{25}$. Then, after Thomas pulls out a ticket, there will be 23 tickets left in the box. The probability that Thomas pulls out a losing ticket is $\frac{23}{24}$. Therefore, the probability that both will pull a losing ticket is $\frac{24}{25}\times\frac{23}{24}=\boxed{\frac{23}{25}}$.

Answer 4

Since the first triangle is replaced before the second shape is pulled out, the probability of pulling out a triangle on the first draw is $\frac{6}{6+4+5}=\frac{6}{15}$. The probability of pulling out a triangle on the second draw, assuming the first shape was replaced, is also $\frac{6}{15}$. Therefore, the probability of pulling out two triangles is $\left(\frac{6}{15}\right)\left(\frac{6}{15}\right)=\frac{36}{225}=\boxed{\frac{4}{25}}$.

Answer 5

To find the number of outcomes in the sample space of rolling two number cubes labeled 1-6, we can use the counting principle. Since each cube has 6 faces, there are 6 possible outcomes for each cube. To find the total number of outcomes when rolling two cubes, we multiply the number of outcomes for each cube together. Therefore, there are $6 \times 6 = \boxed{36}$ outcomes in the sample space.