Respuesta :
Answer:
The probability that the number of correct answers is 4 is 0.2461.
Step-by-step explanation:
Let X = number of correct answers.
The probability that an answer is correct is,P (X) = p = 0.50.
The total number of questions is, n = 9.
The event of an answer being correct is independent of the other answers.
The success of each trial is defined as a correct answer with equal probability of success for each trial, i.e. 0.50.
The random variable X follows a Binomial distribution with parameter n = 9 and p = 0.50.
The probability mass function of X is:
[tex]P(X=x)={9\choose x}\times0.50^{x}\times (1-0.50)^{9-x};\ x=0,1,2,3...[/tex]
Compute the value of P (X = 4) as follows:
[tex]P(X=4)={9\choose 4}\times(0.50)^{4}\times (1-0.50)^{9-4}[/tex]
[tex]=126\times 0.0625\times 0.03125\\=0.24609375\\\approx 0.2461[/tex]
Thus, the probability that the number of correct answers is 4 is 0.2461.
