Question 1087096: Jacob and Ashley run an animal shelter that houses only cats and dogs the ratio of cats to dogs is 5:4 of the cats 40% are kittens while 3/7 of the dogs are puppies the shelter houses a total of 63 animals
1. a group of 6 animals is chosen at random from the shelter what is the probability that the group contains at least one kitten
I already answered this one and got 79.42% chance and found that there are 35 cats 14 of them are kitten and 28 dogs but I don't know how many of them are puppies
2.a group of 8 adult animals is chosen at random from the shelter what is the most likely number of cats and dogs in this group and what is the probability of that arrangement happening. give your probability to 4 decimal places.
---- cats and ---- dogs with a probability of -----
3. a group of 10 baby animals is chosen from the shelter. is the probability distribution for the makeup of this group symmetric or skewed justify your answer
thanks for the help I really just need help with 2 and three but can you let me know if 1 is right or not thanks again
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! 63 animals, an 5:4 cats to dogs; because 63/9 (5+4)=7, the shelter has 35 cats and 28 dogs.
40% of the 35 cats are kittens, which is 14. 3/7 of the dogs are puppies, so that is 12.
If 6 animals are chosen at random, probability NONE is a kitten is
(49/63)*....(44/58)=0.2058; take the complement and get your result of 79.42%
=======================
choosing 8 adult animals, which includes 21 cats and 16 dogs or 37 altogether
Total number of choices is 37C8
The numerator will be of the form 21C4*16C4=10892700
other possibilities are 21C5*16C3=11395540; divide this by 37C8=0.2952
and 21C3*16C5=5809440
check 21C6*16C2=6511680
======================
10 babies are chosen from 14 kittens and 12 puppies. It will be skewed, since there are unequal numbers of both.
Look at the probability of 5 of each, 6 and 4, and 4 and 6
14C5 * 12C5=1585584
14C6*12C4=1486485
14C4*12C6=924924
This is not symmetrical, as expected.
|
|
|
