[Vivienne]

A small quiz from Vernon's show on Saturday:-

There are 2 boxes: in one box are 4 mustard packets, in the second box are 4 ketchup packets.

If, without looking, Big Bad Joe approaches the boxes, and grabs 4 packets, what is the chance (as a percentage), that 3 packets will be mustard?

[Console]

If it was one box with the packets in no particular order (randomised) and all of the packets were the same, then I would say that the percentage probability is roughly 24%, but 'Big Bad' Joe may just deliberately take from all the same box, or may know already where the mustard box is, or the packets could feel different and if he is aiming to get all mustard packets (or, at least, a certain number of a certain packet) then the probability becomes far harder to work out.

[Vivienne]

Well, Vernon K. has a maths quiz every Saturday morning, and the maths teacher he had on air says the probability is 75%.

[Console]

I'd like to know the workings behind that, 'Big Bad' Joe would have to have prior knowledge of where the packets were to have that high a percentage.

[Vivienne]

I don't know.. But R1 say the answer is 75%... there is a small quiz every Saturday around 1000-1030 hours. You would probably enjoy it. Vernon said this is an easy question, compared with some weeks.

Here is another: If Jane earns £13,750, and she is given an increase in her salary of 7%, what would the increase be?

[Zoot]

I don't know.. But R1 say the answer is 75%... there is a small quiz every Saturday around 1000-1030 hours. You would probably enjoy it. Vernon said this is an easy question, compared with some weeks.

Here is another: If Jane earns £13,750, and she is given an increase in her salary of 7%, what would the increase be?

The increase is 7%. You stated this in the quetion.

[Vivienne]

No, but what, as a sum, would 7% be?

[Console]

I doubt I'd enjoy it if the answer is that far off. IF the chance of picking out three mustards if 75%, then the chance for picking out three ketchups is also 75% - as these add up to greater than 100% something is wrong.

Oh, and £962.50.

[Vivienne]

That must have been what R1 meant... the chances are 75% for each... I texted in 50-50 chance (hangs head in shame).

Seriously though, some weeks , I think you would enjoy it, because they have really hard stuff, which few people can get right.

[Console]

That must have been what R1 meant... the chances are 75% for each... I texted in 50-50 chance (hangs head in shame).

I've just worked it out again (on paper this time instead of in my head) and got 35.714% (5/14), which when doubled only makes 71.428% (10/14). Can anyone get the 75% claimed on the show?

[Vivienne]

I can get it, funnily enough, but then I can only count to 100. Seriously though, you'd need to "listen again", if you like, in case I have got this slightly wrong somewhere.

[Vivienne]

The way I see it, is, if you grab 3 pkts randomly, then if each packet is a 3rd (or 25%), then 25 x 3 = 75.

[Yudster]

But that wasn't the question, was it?

[Console]

A third is also not 25%, it's 33%.

[Vivienne]

But if 100 is divided by a quarter, it should be 25%... there were 4 packets, so if 3 were grabbed, 75% should come into a person's hands.

[Console]

There are eight packets though (four mustard and four ketchup) and 'Big Bad' Joe is taking four of them - now, he could take no mustard packets, and four ketchup packets, one mustard packet and three ketchup packets, two of each, three mustard and one ketchup or four mustard and no ketchup. We're looking from the probability of having at least three mustard, so that's the probability of three mustard and one ketchup and four mustard and no ketchup. The probability of having four mustard is 2.85% (1/35), it's just the other bit I seem to be struggling with.

[Zoot]

Right, i'm listening again now

[Vivienne]

Well done, zoots. I was actually half out of a bubble bath, and half in it, at the time I was listening... trying to cope with too many bubbles, the radio, and writing the quiz down all at the same time, so I may be off on one.

[Zoot]

right, the question is -

There are two boxes. Each box has 4 mustard packets and 4 Ketchup packets. you take 1 packet from each box withour looking.
What is the probability that at least ONE of those packets you take out is a mustard packet?

[Vivienne]

I invented "Big Bad Joe" by the way.

[Yudster]

You invented the question as well, didn't you. What zoot said is nothing like what you said. It makes sense now.

[Console]

There are two boxes. Each box has 4 mustard packets and 4 Ketchup packets. you take 1 packet from each box withour looking.
What is the probability that at least ONE of those packets you take out is a mustard packet?

In that case, the answer is 75%. The probability of not taking a mustard out of box 1 is 50%, and the probability of not taking a mustard out of box 2 is also 50%, multiplied together is the chance of not pulling out a mustard out of either box, so, if you take that away from 100%, you're left with 75% for pulling out at least one.

[Vivienne]

Good, it's all resolved.

[foot-loose]

Viv's quizzes are always worth a giggle.

"Whats 2+2?"
"4?"
"NO!"
"Why?"
"I dunno - I heard the answer was 7?!"
"Where?"
"Ediths show, dummy!"
"I've just listened again and the question was 'whats 5+2?'"
"Ahh. That would make sense then!"

[Vivienne]

Love you, Foots.... I think I was trying to do too many things at once: i.e. being covered in foam; listening to radio; trying to write whilst covered in foam, etc... All that, and I'm supposed to absorb a mathematical question...