Suppose we observe a random sequence of letters consisting of four As, five Bs,
ID: 3275342 • Letter: S
Question
Suppose we observe a random sequence of letters consisting of four As, five Bs, eight Cs and three Ds. Under the assumption that all such sequences are equally probable, compute the probability that the random sequence consists of four blocks, with each block containing precisely one of the four letters. Examples: AAAABBBBBCCCCCCCCDDD, DDDBBBBBAAAACCCCCCCC, CCCCCCCCDDDAAAABBBBB, ... In drawing nine cards with replacement from an ordinary deck of 52 cards, what is the probability of drawing three aces of spades? By contrast, What is the probability of obtaining the three aces of spades in precisely the first three draws? A town has five parks. On a Saturday, five classmates, who are unaware of each other's decision, choose a park at random and go there at the same time. What is the probability that at least two of them go to the same park?Explanation / Answer
3)
P( ace spade in 1 attempt) = 1 ace spade out of 52 deck = 1/52
P(3 aces of spades when replacement is allowed) = ?
It is like choosing 3 spades aces in any of the 9 draws.
So, P(3 aces of spades when replacement is allowed) =9C3 * (1/52)^3 *( 51/52)^6
=.0005
In precisly first 3 goes , probabity is equal to gettiing ace of spades in each of the picks = (1/52)^3 = .0000071