# Thread: probability help, ven diagram

1. ## probability help, ven diagram

A study was made of a group of 150 children to determine which of three cartoons they watch on television. The following results were obtained:
• 35 watch Toontime
• 54 watch Porky
• 62 watch Skellingtons
• 9 watch Toontime and Porky
• 14 watch Porky and Skellingtons
• 12 watch Toontime and Skellingtons
• 4 watch Toontime, Porky and Skellingtons
a Draw a Venn diagram to represent these data.
Find the probability that a randomly selected child from the study watches
b none of the three cartoons,
c no more than one of the cartoons.
A child selected at random from the study only watches one of the cartoons.
d Find the probability that it was Skellingtons.
Two different children are selected at random from the study.
e Find the probability that they both watch Skellingtons.
I am stuck on question 9b ,

heres my ven diagram

should the probability that a randomly selected child watched no more than one cartoon = $\frac{ 18 + 35 + 40}{150}$ ?

But the correct answer is $\frac{30+18 +35 +40}{150}$

why do they include 30 into the calculattion? is that not the number that a child watched none of these cartoons?

Also I need help with d and e

thanks!

2. Originally Posted by Tweety
I am stuck on question 9b , Mr F says: 9c you mean.

heres my ven diagram

should the probability that a randomly selected child watched no more than one cartoon = $\frac{ 18 + 35 + 40}{150}$ ?

But the correct answer is $\frac{30+18 +35 +40}{150}$

why do they include 30 into the calculattion? is that not the number that a child watched none of these cartoons? Mr F says: No more than 1 means less than 2. Less than 2 is 1 or none in my book. And there are 30 who watch none.

Also I need help with d and e

thanks!
(d) Conditional probability. The number who only watch one cartoon is 8 + 35 + 40. Out of that number, 40 watch only Skellingtons. Therefore ....

(e) $\frac{62}{135} \cdot \frac{61}{134}$. A tree diagram makes this very clear (use S and S' as your branches).

3. Originally Posted by Tweety
I am stuck on question 9b ,

heres my ven diagram

should the probability that a randomly selected child watched no more than one cartoon = $\frac{ 18 + 35 + 40}{150}$ ?

But the correct answer is $\frac{30+18 +35 +40}{150}$

why do they include 30 into the calculattion? is that not the number that a child watched none of these cartoons?
Yes, it is. And "no more than one" includes none. If they had said "exactly one" or "one and only one" your calculation would be correct. But "0" is certainly NOT "more than one".

Also I need help with d and e

thanks!