Example 5.5. We roll a fair die then toss a coin the number of times shown...
in a game, you toss a fair coin and a fair six sided die. if you toss a heads on the coin and roll either a 3 or a 6 on the die, you win $30. otherwise, you lose $6. what is the expected profit of one round of this game
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.
A coin flip: A fair coin is tossed three times. The outcomes of the three tosses are recorded. Round your answers to four decimal places if necessary. Part 1 of 3 Assuming the outcomes to be equally likely, find the probability that all three tosses are "Heads." The probablility that all three tosses are "Heads" is 0.1250 Part: 1/3 Part 2 of 3 Assuming the outcomes to be equally likely, find the probability that the tosses are all the same....
A2. (a) We roll a fair die twice. Describe a sample space to model this experiment. C4. Consider Problem A2 (a) in Homework 1. Suppose that all the outcomes in the sample space are equally. Let Ai be the event that the sum of the two numbers is greater than 9. Let A2 be the event that both numbers are identical (a) Construct a probability model for this experiment (Specify the general (b) List the outcomes in event A1, and...
1. You roll a die and toss a coin. What is the probability of seeing tails and a 3? 2. You roll a die and toss a coin. What is the probability of seeing a tails or a 3?
If I toss a fair coin 20 times and all 20 tosses result in tails (or “T”), the probability of heads (or "H") appearing on the 21st coin toss is less than 0.5 but greater than 0. 0.5. O 1. O greater than 0.5 but less than 1.
A coin will be tossed twice, and each toss will be recorded as heads ( H ) or tails ( T ). Give the sample space describing all possible outcomes. Then give all of the outcomes for the event that the first toss is heads. Use the format HT to mean that the first toss is heads and the second is tails. If there is more than one element in the set, separate them with commas. Samplespace: Eventthatthefirsttossisheads:
Let N be the number of times we will toss a fair die, where N ∈ Z+ and P(N=k)=0.5^k for any k∈Z+ .Let S be the sum of all the throws of the die. For example, say N turned out to be 5, then we toss the die 5 times. Say the outcomes are 6, 1, 1, 3, 4, 5, then S = 6 + 1 + 1 + 3 + 4 = 15. Calculate P(N = 2 | S...
7. We toss a fair die four times. What is the probability that all tosses produce different outcomes?
A coin will be tossed twice, and each toss will be recorded as heads (H) or tails (T).Give the sample space describing all possible outcomes.Then give all of the outcomes for the event that the second toss is tails.Use the formatHTto mean that the first toss is heads and the second is tails.If there is more than one element in the set, separate them with commas.