Ben, Anna, and Mark are going out on pizza. They can get a pizza with 3 toppings and decide each to pick one topping. The choices of toppings are pepperoni, hamburger, sausage, onions, bell peppers, olives, and anchovies. If they choose at random, what is the probability that they both choose the same topping?
There are 7 possible toppings to choose from. Let's consider Ben's choice first.
The probability that Ben chooses a topping is 1 out of 7 (since there are 7 choices in total).
After Ben chooses a topping, there are now 6 options left for Anna to choose from. The probability that Anna chooses the same topping as Ben is 1 out of 6 (since there are 6 remaining choices).
Likewise, after Ben and Anna have chosen their toppings, there are now 5 options left for Mark to choose from. The probability that Mark chooses the same topping as Ben and Anna is 1 out of 5 (since there are 5 remaining choices).
Therefore, the probability that they all choose the same topping is the product of these individual probabilities: (1/7) * (1/6) * (1/5) = 1/210.
Thus, the probability that they all choose the same topping is 1/210.
To find the probability that they both choose the same topping, let's consider the choices of each person one by one.
Person 1 (Ben) has 7 possible toppings to choose from.
Person 2 (Anna) also has 7 possible toppings to choose from, but since Ben has already made his choice, Anna can only choose from the remaining 6 toppings.
Since both Ben and Anna need to choose from the same toppings, the probability that they choose the same topping can be calculated as follows:
Probability = (Number of favorable outcomes) / (Total number of possible outcomes)
The number of favorable outcomes is when Ben and Anna both choose the same topping. There are 7 possible toppings, so the number of favorable outcomes is 7.
The total number of possible outcomes is the number of choices Ben has multiplied by the number of choices Anna has. This is equivalent to 7 * 6 = 42.
Therefore, the probability that Ben and Anna both choose the same topping is:
Probability = 7 / 42 = 1 / 6 ≈ 0.1667 or 16.67%