When a coin is tossed four times, sixteen equally likely outcomes are possible as shown below: HHHHHHHTHHTHHHTTHTHHHTHTHTTHHTTTTHHHTHHTTHTHTHTTTTHHTTHTTTTHTTTT Let X denote the total number of tails obtained in the four tosses. Create a probability distribution of the random variable X. xP(X)
Question
When a coin is tossed four times, sixteen equally likely outcomes are possible as shown below: HHHHHHHTHHTHHHTTHTHHHTHTHTTHHTTTTHHHTHHTTHTHTHTTTTHHTTHTTTTHTTTT Let X denote the total number of tails obtained in the four tosses. Create a probability distribution of the random variable X. xP(X)
Solution
The random variable X can take on the values 0, 1, 2, 3, 4. These values represent the number of tails that can be obtained when a coin is tossed four times.
To create a probability distribution of the random variable X, we need to find the probability of each value of X.
-
X = 0 (No tails, all heads): There is only 1 outcome (HHHH) out of 16 that has no tails. So, P(X=0) = 1/16.
-
X = 1 (One tail): There are 4 outcomes (HHHT, HHTH, HTHH, THHH) out of 16 that have one tail. So, P(X=1) = 4/16 = 1/4.
-
X = 2 (Two tails): There are 6 outcomes (HHTT, HTHT, HTTH, THHT, THTH, TTHH) out of 16 that have two tails. So, P(X=2) = 6/16 = 3/8.
-
X = 3 (Three tails): There are 4 outcomes (THHT, THTH, TTHH, HTTT) out of 16 that have three tails. So, P(X=3) = 4/16 = 1/4.
-
X = 4 (Four tails): There is only 1 outcome (TTTT) out of 16 that has four tails. So, P(X=4) = 1/16.
So, the probability distribution of the random variable X is:
| X | P(X) |
|---|---|
| 0 | 1/16 |
| 1 | 1/4 |
| 2 | 3/8 |
| 3 | 1/4 |
| 4 | 1/16 |
Similar Questions
When a coin is tossed four times, sixteen equally likely outcomes are possible as shown below: HHHHHHHTHHTHHHTTHTHHHTHTHTTHHTTTTHHHTHHTTHTHTHTTTTHHTTHTTTTHTTTT Let X denote the total number of tails obtained in the four tosses. Find the following probabilities: A. P ( X < 3) = B. P ( X > 2) =
Four unbiased coins are tossed simultaneously. The expected number of heads is :X: 0 1 2 3 4P(x) 1/16 4/16 6/16 4/16 1/16(a) 1(b) 2(c) 3(d) 4
Make an organized list to show all possible outcomes when four fair coins are flipped. Each coin lands facing either heads up (H) or tails up (T). What is the probability that at least three coins land facing tails up?
How many different possible outcomes are there if you flip four coins?
If you flip 4 coins, what is the probability you will get all heads OR all tails, P( all H or all T)?
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.