some quick questions

[ElephantStew]

okay, ive been doing some binomial distribution questions and i can't do 2 of them

1) If a panel of two people is selected at random from the population, 60% of whom are aged 25 years or less. Find he probability that the panel contains the same number of people aged 25 years or less and people aged over 25 years.

2)Suppose that the probability of snow on any day is conditional on whether or not it snowed on the preceding day. The probability that it will snow one day given that it snowed on the preceding day is 5/8, and the probability that it will snow one day given that it did not snow o the preceding day is 2/5. If it snows on Monday, what is the probability it will snow on Wednesday?

kthanks

[cara.mel]

1) You have 4 combinations, OO OY YO YY (Y=young, O=old), you want the OY or YO one
= (.6 * .4) * 2 = 0.48

2) Draw a tree diagram of the situation and work it out that way (unless you're doing methods cas, then you'll learn another way, but tbh you still might as well draw a tree diagram as its two days away)

[Mao]

2)Suppose that the probability of snow on any day is conditional on whether or not it snowed on the preceding day. The probability that it will snow one day given that it snowed on the preceding day is 5/8, and the probability that it will snow one day given that it did not snow o the preceding day is 2/5. If it snows on Monday, what is the probability it will snow on Wednesday?

that's markov chain, basically.

Code: [Select]

Day 1
snow no snow
day 2 snow 5/8 2/5
no snow 3/8 3/5

so basically draw a tree diagram off that.

or, if you are in CAS, using transition matrices: