S1

Q.1 Three married couples stand in a line for a photograph to be taken. Find the number of different ways in which these six people can be arranged if no man stands next to another man.

Q.2 A market sells potatoes whose weights are normally distributed with mean 65 grams and standard deviation 15 grams.
(i) Find the probability that a randomly chosen potato weighs between 40 grams and 80 grams.

I found the answer to this part using the probability districution table and all and the answer was 0.7935 which is correct, however I can't figure out the second part which says :

The market sells potatoes weighing more than 80 grams separately packaged. Potatoes weighing between 80 grams and L grams are labelled large and potatoes wighing over L grams are labelled as extra large.
(ii) Given that a randomly chosen potato is twice as likely to be large as extra large ,calculate the value of L.

Reply 1

nota bene

e-n-i-g-m-a

Q.1 Three married couples stand in a line for a photograph to be taken. Find the number of different ways in which these six people can be arranged if no man stands next to another man.

I might be on the wrong track, but to me it seems like we should consider a couple a 1, hence making the possible arrangements 3!, and then multiply by 2 since you can either start with a male, or a female to the left in the line. I.e. answer is 12... If it is the right answer this is the reasoning... I rely on that someone will correct me if I'm wrong :smile:

Reply 2

e-n-i-g-m-a

No the answer is 144 for the first question.

Reply 3

e-n-i-g-m-a

Help !!!

Reply 4

James

Draw some pictures. You don't necessarily need alternating men and women.

Reply 5

e-n-i-g-m-a

ya ...i got 4 ways to arrange them ...and I figured the answer was 3! * 3! *2! * 2! ..but i'm still confused !

Reply 6

James

e-n-i-g-m-a

ya ...i got 4 ways to arrange them ...and I figured the answer was 3! * 3! *2! * 2! ..but i'm still confused !

What do you mean? That's the answer.

Reply 7

e-n-i-g-m-a

ya but that was for one arrangement ..WMWMWM ...but I came up with for arrangements so shouldn't 144 be multiplied by 4 ?

Reply 8

e-n-i-g-m-a

Help ...

for the second question i tried using normal distribution but it doesn't really seem to work:
P(80<X<L)
P(1<Z<L-65/15) = 2/3
can't go any further

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