Some probability questions i need help with

[xers]

I don't remember exactly word for word but this is roughly how the question is:

Tom works at a coffee shop and he notices that of 10 customers who come into the shop, 4 would not use sugar at all, 3 would use 1 sachet of sugar, 2 would use 2, and 1 would use 3.

a. What is the probability that of the next 3 customers who come in, a total of 2 sachets of sugar are used.
b. The weight of the sugar sachets is normally distributed with a mean of 5.2g and sd of 0.1 g, what is the probability that a customer will use exactly 1 sachet of sugar that weighs under 5g?

[Collin Li]

a. There are six possibilities:

200, 020, 002
110, 101, 011




b. The successful possibilities:

1. The customer uses 1 sachet, which happens to weigh under 5g.
2. The customer uses 2 sachets, one of which happens to weigh under 5g.
3. The customer uses 3 sachets, one of which happens to weigh under 5g.

Let be a normally distributed random variable with .



Evaluate that any way you like. If it is technology free, use the fact that

Hence,

Now, the probability of each branch (1 to 3) are: