A pizza parlor has 13 different toppings available for its pizzas, and 2 of these toppings are pepperoni and anchovies. If a customer picks 2 toppings at random, find the probability that pepperoni is one of the toppings.
Round to four decimal places.
Probability of picking pepperoni on the first pick = 1/13.
Assuming that customer does not want to "double up" on any topping, 12/13 for first pick for some other topping and 1/12 for second for pepperoni. If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.
Either-or probabilities are found by adding the individual probabilities to combine with first sentence results.
292
To find the probability that pepperoni is one of the toppings, we need to determine the number of favorable outcomes (picking pepperoni) and the total number of possible outcomes (picking any two toppings).
The number of favorable outcomes is 1, as there is only one pepperoni topping available.
The total number of possible outcomes can be calculated using the formula for combinations:
nCr = n! / (r!(n-r)!)
Here, n = 13 (total number of available toppings) and r = 2 (number of toppings to be picked).
Plugging in the values, we get:
13C2 = 13! / (2!(13-2)!)
= 13! / (2!11!)
= (13 * 12 * 11!) / (2! * 11!)
= (13 * 12) / 2
= 78
Therefore, there are 78 possible outcomes when picking any two toppings.
Now, we can find the probability by dividing the number of favorable outcomes by the total number of possible outcomes:
Probability = Number of favorable outcomes / Total number of possible outcomes = 1 / 78
Rounding to four decimal places, the probability that pepperoni is one of the toppings is approximately 0.0128.
To find the probability that pepperoni is one of the toppings, we need to determine the total number of possible outcomes and the number of favorable outcomes.
Total number of possible outcomes:
Since there are 13 different toppings available, and the customer is picking 2 toppings, we can calculate this using combination formula (nCr):
Total possible outcomes = 13C2 = (13!)/(2!(13-2)!) = (13!)/(2!11!) = (13*12)/(2*1) = 78
Number of favorable outcomes:
For pepperoni to be one of the toppings, the customer can choose pepperoni as the first topping and any one of the remaining 12 toppings as the second topping. Therefore, the number of favorable outcomes is 1 * 12 = 12.
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 12/78
Probability = 0.1538 (rounded to four decimal places)
So, the probability that pepperoni is one of the toppings when the customer picks 2 toppings at random is approximately 0.1538.