


Draw a tree diagram displaying all possible outcomes given a roll of a six sided die,...
(a) Draw a tree diagram to display all the possible outcomes
that can occur when you flip a coin and then toss a die.
(b) How many outcomes contain a head and a number greater than
4?
(c) Probability extension: Assuming the outcomes displayed
in the tree diagram are all equally likely, what is the probability
that you will get a head and a number greater than 4 when you flip
a coin and toss a die? (Round your answer...
If I flip a coin and roll a six sided die simultaneously, the SAMPLE SPACE of this experiment holds ________ possible unique outcomes. A.36 B.24 C.12 D.8
You roll a 6-sided die. What is the probability that you will roll either a 3 or a 2? P (3 or 2) = You flip a 2-sided coin. What is the probability that you will get either heads or tails? P (heads or tails) =
Let W be a function that takes the result of a six-sided die roll and multiplies it by 0 if a coin lands Heads, and 1 if it lands Tails. What is the distribution over W? What is the expectation?
Construct a sample space (list or make a tree diagram of all of the outcomes) for the experiment of a) rolling a 12 sided die and flipping a coin at the same time. Assuming each outcome is equally likely, what is the probability of: DO NOT REDUCE b) rolling a number less than 4 and getting heads? c) rolling an odd number and getting tails? d) rolling a 7 and getting ( heads or tails)
1) Suppose we have a fair 6 sided die and a coin. a) If we roll the die 4 times, the total number of possible outcomes is? b) If we roll the die 2 times then flip the coin 3 times, the total number of possible outcomes is? Show your calculations.
We flip a coin. If it is heads we roll a four sided die with sides numbered from 1 to 4. If it is tails, we roll a six sided die with sides numbered from 1 to 6. We let X be the number rolled. (a) What is the expectation of X? (b) What is the variance of X? (c) What is the standard deviation of X? We draw cards one by one and with replacement from a standard deck...
For the two six-sided dice case: Write out the six-by-six matrix showing all possible (36) combinations of outcomes. Draw a histogram of the probability of outcomes for the dice totals. Explain the shape of the histogram. Draw a Venn diagram for the 36 dice roll combinations. Define a set "A" as all the combinations that total seven; define set "B" as all the combinations that have one die roll (either die 1 or 2) equal to 2. Indicate the sets...
Consider the setting where you first roll a fair 6-sided die, and then you flip a fair coin the number of times shown by the die. Let D refer to the outcome of the die roll (i.e., number of coin flips) and let H refer to the number of heads observed after D coin flips. (a) Suppose the outcome of rolling the fair 6-sided die is d. Determine E[H|d] and Var(H|d). (b) Determine E[H] and Var(H).
1. Consider the experiment: You flip a coin once and roll a six-sided die once. Let A be the event that you roll an even number and B be the event that you flip heads. (a) Determine the sample space S for this experiment. (Hint: There are 12 elements of the sample space.) (b) Which outcomes are in A? (c) Which outcomes are in B? (d) Which outcomes are in A'? What does it mean in words? (e) Which outcomes...