probability trees (1 Viewer)

[Instinct77]

hey guys can someone tell me how to workout a prob question when it uses percentages rather than fractions for example;

"the probability that sarah will pass next weeks assesment item is 90% and the probability that carl will pass is 60% what is the probility that:

they will both pass?
carl will pass and sarah will fail
at least one of them will fail?

im fine with fractions but have no idea with the % questions.

 

[tahlsy31191]

Just convert them to fractions then work with the question.

 

[savio23q]

90% as a fraction is just 9/10.
60% is 6/10.

So...

(i) 9/10 x 6/10 = 27/50

(ii) Probability that Sarah will fail = 1/10
Probability that Carl will pass = 6/10

i.e. 1/10 x 6/10 = 3/50

(iii) This one requires a tree.

I cant be bothered drawing one and posting it up so i'll try to explain with words.

There are 4 different possibilities.

Sarah passes, Carl passes
Sarah passes, Carl fails
Sarah fails, Carl passes
Sarah fails, Carl fails.

i.e. the probability that AT LEAST one fails is 23/50.

Hope that helps.

 

[Instinct77]

thanks, i got it now.

cheers for the help, much appreciated!

 

[cheechthecheech]

i.e. the probability that AT LEAST one fails is 23/50.

The answer for iii) is infact 0.42 or 21/50.

 

[PC]

hey guys can someone tell me how to workout a prob question when it uses percentages rather than fractions for example;

"the probability that sarah will pass next weeks assesment item is 90% and the probability that carl will pass is 60% what is the probility that:

they will both pass?
carl will pass and sarah will fail
at least one of them will fail?

im fine with fractions but have no idea with the % questions.

Remember that these are overall statistics, rather than a physical count, so when using a tree, take care NOT to reduce the fractions.

For this I'd just use decimals rather than fractions.

(a) P(both pass) = 0.9 x 0.6 = 0.54 = 54% = 27/50

(b) P(Carl pass, Sarah fail) = 0.6 x 0.1 = 0.06 = 6% = 3/50

(c) P(at least one fail) = 1 – P(both pass) = 1 - 0.54 = 0.46 = 46% = 23/50