Statistics 1 - AQA Maths Simple Probabilities

I've just come across the following Stats question. I'm pretty rusty and I don't really know how to work part ii) or iii) out. The mark scheme just confuses me as I don't know what they're doing.

If anyone could actually explain to me what the question is asking and why and how it is worked out it would be extremely useful. I have tried to construct a tree diagram but they seem to be two separate events so I didn't know how to.

A health club has a number of facilities which include a gym and a sauna. Andrew and his wife, Heidi, visit the health club together on Tuesday evenings. On any visit, Andrew uses either the gym or the sauna or both, but no other facilities.

The probability that he uses the gym, PðGÞ, is 0.70 .
The probability that he uses the sauna, PðSÞ, is 0.55 .
The probability that he uses both the gym and the sauna is 0.25 .

i) he does not use the gym;
ii) he uses the gym but not the sauna;
iii) he uses either the gym or the sauna but not both.

Thank you to anyone who can help! And merry Christmas. :smile:

Try using this:

OP

Original post by XShmalX

Try using this:

Ah, that makes much more sense. Thank you.

Out of interest, is there a rule that will help me to know whether to use a ven diagram or a tree diagram? Like the ones that use a ven diagram seem to be slightly different questions, is there something I should look out for to tell me it's one type instead of the other?

Thanks again. :smile:

Reply 3

Flint_09

8

Original post by XShmalX

Try using this:

hello mate, could i ask you a probablity question, i appreciate your help,

the question is

A new housing development contains 100 properties of which 40 are semi-detached houses, 25 are detached houses, 20 are semi-detached bungalows and 15 are detached bungalows. a property is selected at random. Determine the probability that the property selected is:

a. either detached or a bungalow or both
i could do it if it were detached or a bungalow but 'or both' is confusing me.

thanks

Reply 4

XShmalX

1

Original post by themagicpiano

Ah, that makes much more sense. Thank you.

Out of interest, is there a rule that will help me to know whether to use a ven diagram or a tree diagram? Like the ones that use a ven diagram seem to be slightly different questions, is there something I should look out for to tell me it's one type instead of the other?

Thanks again. :smile:

Well the main thing is in this case we can see the sum of the two probabilities is greater than 1 so we know there must be an overlap.

Reply 5

XShmalX

1

Original post by Flint_09

hello mate, could i ask you a probablity question, i appreciate your help,

the question is

A new housing development contains 100 properties of which 40 are semi-detached houses, 25 are detached houses, 20 are semi-detached bungalows and 15 are detached bungalows. a property is selected at random. Determine the probability that the property selected is:

a. either detached or a bungalow or both
i could do it if it were detached or a bungalow but 'or both' is confusing me.

thanks

The or both mean you want to include the15 detached bungalows as well.

Statistics 1 - AQA Maths Simple Probabilities

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