Probability word problem

Question

Of a group of 30 cats, 24 eat tinned or dry food, 10 like dry food and 5 like both tinned and dry food. Find the probability that a selected cat likes only tinned food.

 

Answer 7/15, but how do you do it?

Answer 1

draw 2 intersecting circles and mark one T and mark one D

24 eat tinned or dry food

10 like dry so put 10 in the circle marked D but outside the intersection

5 like both so put 5 in the intersection but change the 10 in the D part only to a 5 because 5 in the intersection plus 5 in the D part only makes the 10

so now you have two intersecting circles with 5 in the intersecting part and 5 in the D only part

24 cats eat dry or tinned, so there are 24-10=14 cats unaccounted for

put 14 in the T part only of the diagram

14 in the T only, 5 in the intersection, and 5 in the D only for a total of 24 cats

probability that a cat likes only tinned:

14 cats are in the T part only and there are 30 cats

P(tinned)=14(like tinned only)/30(total number of cats)=14/30=7/15 after simplifying

Answer 2

Hello Chrissy,

 

The answer could be as following: the conditional probability that selected cat eats tinned or dry food is 24/30. Additionally, the probability that within this group the cat like only tinned food is 14/24. Multiplying this two gives the answer:

(24/30)*(14/24) = 7/15

Best regards,