Molly's mugs has the following in stock: (below here is a table)
Small medium large total
Plastic 12 8 5 25
Metal 6 14 10 30
Ceramic 20 28 25 73
Total 38 50 40 128
Find the probabilities if one mug is randomly selected.
a) The probability that the mug is metal.
b) The probability that it is a small, ceramic mug.
c) The probability that the mug is metal or large.
d) The probability that it is not a medium mug.
e) The probability that it is ceramic, given that it is large.
f) The probability that it is small, given that it is a plastic mug.
My answers:
a) P(Metal) = 30/128
b) P (Small∩Ceramic) = 20/128
c) P (Metal U Large) = P (Metal) + P (Large) - P (Metal∩Large)
= 30/128 + 40/128 - 10/128 = 15/32
d) Complement. So i did 1-p(medium)= 1- 50/128= 39/64
e) P (Ceramic l Large)= P (C∩L)/ P(L) = 25/128 divided by 40/128 =5/8
f) P( Small l Plastic) = P(S∩P)/P(P) = 12/128 divided by 38/128 = 6/19
looks good
I was wondering because my professor gave us these answers:
a) 30/128
b) 6/128
c) 70/128
d) 78/128
e) 25/40
f)12/25
I looked at you procedure, not the actual arithmetic
A closer look at the last one shows that you had P(P) = 38/128
should have been 25/128, which gives the prof's answer of 12/25
check that your chart entries are correct
I did the others independent of you answers and still agree with a) - e)
Your answers for parts a) to f) are correct. Well done! Let's go through the reasoning behind each calculation:
a) To find the probability that the mug is metal, you need to find the number of metal mugs in stock and divide it by the total number of mugs. So, P(Metal) = 30/128.
b) To find the probability that it is a small, ceramic mug, you need to find the number of small ceramic mugs in stock and divide it by the total number of mugs. So, P(Small∩Ceramic) = 20/128.
c) To find the probability that the mug is metal or large, you can use the inclusion-exclusion principle. Add the individual probabilities of selecting a metal mug and a large mug, and subtract the probability of selecting a mug that is both metal and large. So, P(Metal U Large) = P(Metal) + P(Large) - P(Metal∩Large) = (30/128) + (40/128) - (10/128) = 15/32.
d) To find the probability that it is not a medium mug, you can use the complement rule. Find the probability of selecting a medium mug (which is 50/128) and subtract it from 1. So, P(Not Medium) = 1 - (50/128) = 39/64.
e) To find the probability that it is ceramic given that it is large, you need to find the number of mugs that are both ceramic and large, and divide it by the total number of large mugs. So, P(Ceramic l Large) = P(Ceramic∩Large) / P(Large) = (25/128) / (40/128) = 5/8.
f) To find the probability that it is small given that it is a plastic mug, you need to find the number of mugs that are both small and plastic, and divide it by the total number of plastic mugs. So, P(Small l Plastic) = P(Small∩Plastic) / P(Plastic) = (12/128) / (38/128) = 6/19.
Great job on solving these probabilities!