An ice-cream parlor sells sundaes with 3 different types of ice-cream and 4 different toppings. They have 8 flavors of ice-cream and 10 toppings for their customers to chose from.what is the probability that a customer orders a sundae including chocolate and strawberry ice cream?
Hm..
There are 3 different types (brands?) ice creams EACH with 8 flavours, and 4 types (styles?) of toppings EACH with 10 flavours.
In all, there are 3*8=24 different ice creams and 4*10=40 toppings, for a total sample space of 40*24=960 items.
Given that the ice cream has chocolate OR strawberry (nothing in the questions says we can combine flavours), it is 2 flavours out of 8 ice cream flavours.
The probability is therefore 2/8=1/4.
I tried that already, it didn't work.
Did you copy the question word for word, or did you paraphrase it?
It does not appear too clear for me about the 3 types of ice cream and 4 types of toppings apart from the flavour. Also, the qustion did not mention about multiple flavours, yet it asks for chocolate AND strawberry.
Please check wording of the question before going further.
To find the probability that a customer orders a sundae including chocolate and strawberry ice cream, we need to determine the total number of possible combinations and the number of combinations that include both chocolate and strawberry ice cream.
First, let's calculate the total number of possible combinations. There are 8 flavors of ice cream and a customer can choose any 3 flavors for their sundae. We can calculate this using the combination formula:
C(n, r) = n! / (r! * (n-r)!)
Where n is the total number of options and r is the number of options chosen.
In this case, n = 8 (flavors of ice cream) and r = 3 (flavors chosen for the sundae).
C(8, 3) = 8! / (3! * (8-3)!) = 8! / (3! * 5!) = (8 * 7 * 6) / (3 * 2 * 1) = 56
So there are 56 total possible combinations of 3 flavors.
Now, let's calculate the number of combinations that include both chocolate and strawberry ice cream. Since we want both chocolate and strawberry in the sundae, we have fixed two of the choices and we need to choose one more flavor from the remaining options.
There are 6 remaining flavors (excluding chocolate and strawberry) and we need to choose 1 from those 6.
This can be calculated using the combination formula:
C(n, r) = n! / (r! * (n-r)!)
In this case, n = 6 (remaining flavors) and r = 1 (additional flavor chosen for the sundae).
C(6, 1) = 6! / (1! * (6-1)!) = 6! / (1! * 5!) = (6 * 5 * 4 * 3 * 2 * 1) / (1 * 5 * 4 * 3 * 2 * 1) = 6
So there are 6 combinations that include both chocolate and strawberry ice cream.
Finally, we can calculate the probability by dividing the number of combinations that include both chocolate and strawberry ice cream by the total number of possible combinations:
P = Number of combinations with both chocolate and strawberry / Total number of combinations
P = 6 / 56 = 3 / 28 ≈ 0.107 or 10.7% (rounded to one decimal place)
Therefore, the probability that a customer orders a sundae including chocolate and strawberry ice cream is approximately 0.107 or 10.7%.