Could I please have some help with this conditional probability question

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L1232

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Hi I know this question is probably fairly simple but i haven't been able to get the right answer. The question is...
Laura has 9 tins of soup in her cupboard but all the labels are missing. She knows 6 of the tins have vegetable soup and the other 3 have tomatoe soup. She picks three tins at random. What is the the probability that she picks more vegetable soup compared to tomatoe soup?leave your answer to 2 decimal places

This question is on a maths app and it has said the answer is 0.81
Could someone please show how to get to that answer for me so I can see where I went wrong or what I didn't do. Thanks
 
This isn't a conditional probability question. It is a binomial distribution question. Have you learnt about binomial probability functions?
 
L1232 said:
Hi I know this question is probably fairly simple but i haven't been able to get the right answer. The question is...
Laura has 9 tins of soup in her cupboard but all the labels are missing. She knows 6 of the tins have vegetable soup and the other 3 have tomatoe soup. She picks three tins at random. What is the the probability that she picks more vegetable soup compared to tomato soup?leave your answer to 2 decimal places. This question is on a maths app and it has said the answer is 0.81
Click to expand...
What is the probability of no tomato or exactly one tomato tin?
 
Harry_the_cat said:
This isn't a conditional probability question. It is a binomial distribution question. Have you learnt about binomial probability functions?
Click to expand...
I must be missing something? How is this a sequence of independent events?
 
JeffM said:
I must be missing something? How is this a sequence of independent events?
Click to expand...
No Jeff you have missed nothing. While it is definitely not conditional probability it is also not binomial probability.
Binomial probability is a sequence of independent events in which the sampling is with replacement. For example, flipping a coin or tossing a die.
Each time a die is tossed it replaces its state. Toss the die ten times, what is the probability of exactly three ones?:\(\displaystyle \dbinom{10}{3}\left(\dfrac{1}{6}\right)^3\left(\dfrac{5}{6}\right)^7\)
However, the question at hand is a simple computational probability without replacement .
The probability that she selects no tomato tins is \(\displaystyle \dfrac{\dbinom{6}{3}}{\dbinom{9}{3}}\) SEE HERE FOR HELP.
 
Wouldn't one normally use the hypergeometric distribution for this? If [MATH]T[/MATH] = number of tomatoes drawn then
[MATH]P(T=x) = \frac{ \dbinom{3}{x} \dbinom{6}{3-x} } { \dbinom{9}{3} },~x=0\dots 3[/MATH]and you want [MATH]P(T=0)+P(T=1)[/MATH]? And I don't get [MATH].81[/MATH].
 
If she picks more veg than tomato then she must pick either
1. 3 veg
Or
2. 2 veg and a tom

P(3 veg) = 6/9 × 5/8 × 4/7
P(2 veg and a tom) = 6/9 × 5/8 × 3/7 × 3

Add these together to get the answer you need. 0.81 is incorrect.
 
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