Answer: [tex]\bold{\dfrac{125}{1296}}[/tex]
Step-by-step explanation:
The probability of NOT getting a 4 means the probability of getting a 1, 2, 3, 5, or 6 which is 5 out of 6 = [tex]\dfrac{5}{6}[/tex]
The probability of getting a 4 is 1 out of 6 = [tex]\dfrac{1}{6}[/tex]
The probability of getting a 4 only on the last roll is:
NOT 4 and NOT 4 and NOT 4 and Yes 4
[tex]\dfrac{5}{6}[/tex] x [tex]\dfrac{5}{6}[/tex] x [tex]\dfrac{5}{6}[/tex] x [tex]\dfrac{1}{6}[/tex] = [tex]\dfrac{5^3}{6^4}= \dfrac{125}{1296}[/tex]
The probability of getting a 4 only on the last trial is 125/1296. Computed using the binomial distribution.
The probability of an event is the ratio that determines the chance of occurrence of that event.
If A is an event, n is the number of favorable outcomes to event A, and S is the total number of possible outcomes in the experiment, then the probability of event A is given as:
P(A) = n/S.
The binomial distribution is the probability that precisely x successes will occur on n subsequent trials with p probability, as determined by:
P(X = x) nCx.pˣ.qⁿ⁻ˣ, where q = 1 - p.
nCx is determined by how many possible ways there are to combine x items from a collection of n components, and is given as:
nCx = n!/{x!(n - x)!}.
In the question, we are asked to find the probability of getting a 4 only on the last trial, in the experiment of rolling a six-sided fair die 4 times.
Assuming the event of getting a 4 on the dice as success, we can write p = 1/6.
So, we get, q = 1 - p = 5/6. n = 4, the number of times the dice are rolled.
Thus, we get the he binomial distribution, P(X = x) = 4Cx.(1/6)ˣ.(5/6)⁴⁻ˣ.
We are asked to find the probability of getting a 4 only on the last trial, that is, only one success, so we put x = 1, to get:
P(X = 1) = 4C1.(1/6)¹(5/6)⁴⁻¹ = 4.(1/6)(125/216) = 500/1296.
This is the probability of getting a 4 at any throw.
To get the probability of getting a 4 at only the last throw, we divide this by 4, to get,
Probability(4 only on the last throw) = (500/1296)/4 = 125/1296.
Thus, the probability of getting a 4 only on the last trial is 125/1296. Computed using the binomial distribution.
Learn more about Binomial Distribution at
https://brainly.com/question/24756209
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