Probability

2. Sally is at her house, and is going to toss a coin repeatedly. You are talking to Sally on the phone. After each toss of the coin, she will tell you (truthfully) whether the coin came up heads or tails. You know that Sally has a trick 2-headed coin, but you don't know whether she is going to toss that trick coin or an ordinar ...continues

Solution please

3. There are 13 standard decks of cards. Each deck is shuffled, separately. The 13 decks are lined up in a row on the table. The top card is drawn from each deck. What is the probability that at least 3 cards of each suit are drawn?

Probability - cards

4. A hand of 5 cards contains 2 red cards and 3 black cards. Trish plays the following game: A card is drawn from the hand. If the card is red, the game stops immediately. If the card is black, this black card is set aside and a red card is put into the hand in its place. Then another card is drawn from the hand and the same pro ...continues

Probability density function

5. Let E be the event that the number which comes up when a single die is tossed is divisible by 3. Let X be the number of times that event E occurs in 3 tosses of the die. (a) Make a table showing the pdf and the cdf of X. (b) Find E(X) and V(X).

Solution please

6. Use the Binomial tables to find the following values: (a) Pr[B(10, .3)>4] (b) Pr[3≤B(7, .2) (less than) 6] (c) Pr[B(12, .6) ≥7]

Probability - drawing tokens

7. There are some tokens in a bag. Each token has a number ( a positive integer) printed on it. Ernesto does not know how many tokens are in the bag, and the only thing he knows about the numbers on them is that the mean of the numbers is 3 and the variance is 2. Ernesto is going to play a game in which he draws 1 token from th ...continues

Independent random variables

1. A coin is tossed 3 times. Discrete random variable X is equal to the number of times Heads comes up. Discrete random variable Y has the value 1 if the first toss comes up heads and 0 otherwise. (a) Find Pr[(X=1)n(y=1)] Are X and Y independent random variables?

Counting techniques

I am having a hard time trying to understand an example problem in my math book. The problem goes: In how many ways can 3 white tiles, 2 blue tiles, and 2 red tiles be arranged in a single row?( I also need to assume that the tiles are identical except for color.)

Probability of Defective Bulbs : Applying the Binomial Distribution

If there 5 defective bulbs in the batch of 50 bulbs, what is the probability that the sample will have 2 defective bulbs?

Conditional Probability and Independent Events

Given P(A)=.5, P(B)=.3 and the P(AuB)=.7 find the following 1. P(A') 2. P(A| B') 3. P(AnB)