1- Two coins are flipped, followed by rolling a die as many times as the number...

1-

Two coins are flipped, followed by rolling a die as many times as the number
of heads shown.
(a) What is the probability of getting fewer than 5 dots in total?
(b) Given that there were exactly 3 dots in total, what is the conditional
probability that the coins showed exactly one head?

2-

Four people are dealt 13 cards each. You (one of the players) got one ace.
What is the probability that your partner has the other three aces?

3-

Two shooters are shooting two shots each at a target. The probability of the
event “the first shooter hits the target” is 0.7 for each shot and the probability for
the second shooter is 0.8. What is the probability of both shooters missing the
target?

4-

Suppose the experiment consists of rolling two dice (red and green), the event
A is: “the total number of dots equals 6”, B is: “the red die shows an even number”.
Compute P(B/A).

Expert Solution

orchestra answered 2 years ago

A die is weighted so that rolling a 1 is two times as likely as rolling...

A die is weighted so that rolling a 1 is two times as likely as rolling a 2, a 2 is two times likely as rolling a 3, a 3 is two times as likely as rolling a 4, a 4 is two times a likely as rolling a 5, and a 5 is two times as likely as rolling a 6. What is the probability of rolling an even number?

Consider an experiment where fair die is rolled and two fair coins are flipped. Define random...

Consider an experiment where fair die is rolled and two fair coins are flipped. Define random variable X as the number shown on the die, minus the number of heads shown by the coins. Assume that all dice and coins are independent. (a) Determine f(x), the probability mass function of X (b) Determine F(x), the cumulative distribution function of X (write it as a function and draw its plot) (c) Compute E[X] and V[X]

If a heads is flipped, then the coin is flipped 4 more times and the number...

If a heads is flipped, then the coin is flipped 4 more times and the number of heads flipped is noted; otherwise (i.e., a tails is flipped on the initial flip), then the coin is flipped 3 more times and the result of each flip (i.e., heads or tails) is noted successively. How many possible outcomes are in the sample space of this experiment?

Find the probability that: Rolling a fair die 3 times, at least two dice are less...

Find the probability that: Rolling a fair die 3 times, at least two dice are less than 4. Previous answers have suggested 0.875 (189 feasible cases/ 216 total cases). However, from simple trial and error we can see that there are more than 27 cases where this answers fails. For example is the first dice gets a 4 and the 2nd dice gets 4,5,6 and the last dice gets any number, there is already 18 cases here that are not...

Two fair coins are flipped at the same time. 1) What is the probability of getting...

Two fair coins are flipped at the same time. 1) What is the probability of getting a match (same face on both coins)? Answer for part 1 [The answer should be a number rounded to five decimal places, don't use symbols such as %] 2) What is the probability of getting at least two heads? Answer for part 2 [The answer should be a number rounded to five decimal places, don't use symbols such as %]

1)Probability A) A fair coin is flipped three times. How many simple events are there in...

1)Probability A) A fair coin is flipped three times. How many simple events are there in the uniform sample space? List them. B) A fair coin is flipped five times. How many simple events are there in the uniform sample space? C) A fair dice is rolled 10 times. What is the probability it lands on a 6 exactly 3 times? D) A dice is rolled 10 times. What is the probability that it lands on an even number exactly...

An experiment consists of rolling 1 red die, 1 white die, and 1 blue die and...

An experiment consists of rolling 1 red die, 1 white die, and 1 blue die and noting the result of each roll. The dice are fair, and all out comes are equally likely, What is the probability that the SUM of the results on the three dice is 7? What is the probability that the sum is an odd number? Please explain in detail.

Three fair coins are flipped independently. Let X be the number of heads among the three...

Three fair coins are flipped independently. Let X be the number of heads among the three coins. (1) Write down all possible values that X can take. (2) Construct the probability mass function of X. (3) What is the probability that we observe two or more heads. (i.e., P(X ≥ 2)) (4) Compute E[X] and Var(X).

1. Four coins are tossed 11 times. The number of heads is counted and the following...

1. Four coins are tossed 11 times. The number of heads is counted and the following data is reported: 4, 3, 2, 0, 3, 3, 1, 2, 3, 2, 1. Calculate the following sample statistics. Be sure to provide a formula for your answer. a. Sample mean? b. Sample median? c. Sample mode? d. Sample range? e. Sample variance?

How many times of “3” are expected to get in rolling an unloaded dice 50 times?...

How many times of “3” are expected to get in rolling an unloaded dice 50 times? Select one: a. 25 times b. 8 times c. 16.67 times d. 8.33 times

Question