Respuesta :
Answer:
The answer is 0.23(approx).
Step-by-step explanation:
The given die is a three sided die, hence, there are only three possibilities of getting the outcomes.
We need to find the probability of getting exactly 3s as the result.
From the sequence of 6 independent rolls, 2 rolls can be chosen in [tex]^6C_2 = \frac{6!}{2!\times4!} = \frac{30}{2} = 15[/tex] ways.
The probability of getting two 3 as outcome is [tex]\frac{1}{4} \times\frac{1}{4} = \frac{1}{16}[/tex].
In the rest of the 4 sequences, will not be any 3 as outcome.
Probability of not getting a outcome rather than 3 is [tex]1 - \frac{1}{4} = \frac{3}{4}[/tex].
Hence, the required probability is [tex]15\times\frac{1}{16}(\frac{3}{4})^4 = \frac{1215}{4096}[/tex]≅0.2966 or, 0.23.
Binomial distribution has only two possible outcomes. The probability that exactly two of the 6 rolls result in a 3 is 0.131835.
What is Binomial distribution?
A common discrete distribution is used in statistics, as opposed to a continuous distribution is called a Binomial distribution. It is given by the formula,
[tex]P(x) = ^nC_x p^xq^{(n-x)}[/tex]
Where,
x is the number of successes needed,
n is the number of trials or sample size,
p is the probability of a single success, and
q is the probability of a single failure.
We know that the probability of coming a three when the dice is rolled is 1/4(0.25), also, given that the probability of not being coming three, therefore, the probability of the outcome being one and two is 1/2 and 1/4 respectively. therefore,
The probability of three as an outcome is 0.25,
The probability of three not coming as an outcome is [tex]\dfrac{1}{2} +\dfrac{1}{4} = \dfrac{3}{4}=0.75[/tex].
As we can see that there are only two outcomes possible, either 3 will come or three will not come, therefore, we can apply binomial distribution here, where
The probability of 3 as result, p = 0.25
The probability of three is not the result, q = 0.75
Substituting the values in the formula of the binomial distribution for 2 success,
[tex]\begin{aligned}P(X=2) &= ^6C_3 (0.25)^3 (0.75)^{(6-3)}\\& = 20 \times 0.015625 \times 0.421875\\& = 0.131835 \end{aligned}[/tex]
Hence, the probability that exactly two of the 6 rolls result in a 3 is 0.131835.
Learn more about Binomial Distribution:
https://brainly.com/question/12734585
