SANJEET GUPTA:
Hello, I'm Sanjeet Gupta with your weather update.

SANJEET GUPTA:
Not a very exciting week of weather ahead of us, it's a bright start to the morning, but it's not to last.

SANJEET GUPTA:
As we head through the next 24 hours, there will be a mix of sunshine and showers. And with strong winds across the English Channel, it will be feeling cooler in the South.

SANJEET GUPTA:
Scotland, Northern Ireland, it's a better day for you, with highs of 18, and further east, it will be drier with clear skies.

SANJEET GUPTA:
So, what's the probability of it raining today?

SANJEET GUPTA:
Well, the probability of an outcome can have any value between zero, which is impossible, and one, which is certain to occur.

SANJEET GUPTA:
This could be a fraction, decimal, or percentage.

SANJEET GUPTA:
Last year, it rained 12 days out of the 31 days of July. So the relative frequency for the number of days of rainfall is the number of times this outcome occurs, which is the rainfall, divided by the total number of outcomes, which is the total number of days.

SANJEET GUPTA:
So, the estimated probability of rainfall this month is 12 over 31, which equals 0.39 which, on our probability scale, is Not Likely.

SANJEET GUPTA:
So what's the probability of it not raining? Well, all probabilities must add up to one. So we subtract 0.39 from one, which equals 0.61. Which, on our probability scale, is Likely.

SANJEET GUPTA:
But, as it's the UK, our summer came and went last week. So if you're out and about, I'd take a brolly with you, as it's probably going to rain.

UNKNOWN MALE #1:
Fingers crossed for tomorrow, then.

UNKNOWN MALE #2:
I know, yep.

UNKNOWN MALE #1:
Yeah.

UNKNOWN MALE #3:
Help yourself, guys. Have one.

UNKNOWN MALE #1:
'Why would you ruin a chocolate by putting lemon in it? And Turkish delight, there's just no need for that.

UNKNOWN MALE #1:
'They're both going to take one before me, so the probability of my choice is conditional, as it is dependent on the previous outcome. Conditional probabilities can be represented with a tree diagram.

UNKNOWN MALE #1:
'There are five chocolates in total, three I like, and two that I dislike. To calculate the probabilities, I multiply along the branches for the outcome.

UNKNOWN MALE #1:
'And the sum of the probabilities of any set of branches will always be one.

UNKNOWN MALE #1:
'So the probability that they both take a chocolate that I like will be three over five multiplied by two over four, which equals three over ten.

UNKNOWN MALE #1:
'The probability of one person taking a chocolate I like, and the other taking one I dislike, has more than one possibility. So I have to multiply along the branches to find each probability and then add the outcomes together.

UNKNOWN MALE #1:
'So three over five multiplied by two over four, plus two over five multiplied by three over four, equals six over 20, plus six over 20, which equals 12 over 20, which can be simplified to three over five.

UNKNOWN MALE #1:
'That's OK. There's still two left.'

UNKNOWN MALE #2:
Mmm. That's alright, that is.

UNKNOWN MALE #1:
'What the heck? He said take one! Oh, we are no longer friends.'

UNKNOWN MALE #3:
Have one.

UNKNOWN MALE #1:
No thanks, I'm good.

UNKNOWN MALE #3:
Don't be silly. Take one.

UNKNOWN MALE #1:
'Terrible every time. Every time.'

UNKNOWN MALE #3:
There's only one left, you might as well finish the box.