Respuesta :
The probability that the answers fewer than 2 questions correctly in the last 6 questions is 53.392% and this can be determined by using the given data.
Given :
- Ira ran out of time while taking a multiple-choice test and plans to guess on the last 6 questions.
- Each question has 4 possible choices, one of which is correct.
- Let X= the number of answers Ira correctly guesses in the last 6 questions.
The following steps can be used in order to determine the probability that the answers fewer than 2 questions correctly in the last 6 questions:
Step 1 - There are 6 questions and in each question, there are 4 options so the value of 'p' is:
[tex]\rm p=\dfrac{1}{4}=0.25[/tex]
Step 2 - The probability is given by the formula:
[tex]\rm P(X=x)=\;^nC_x(p)^x(1-p)^{n-x}[/tex]
Step 3 - The probability that Ira answers exactly 1 question correctly in the last 6 questions is given by:
[tex]\rm P(X=1)=\;^6C_1(0.25)^1(0.75)^{6-1}[/tex]
[tex]\rm P(X=1)=\;^6C_1(0.25)^1(0.75)^{5}[/tex]
P(X = 1) = 0.35595
Step 4 - The probability that Ira answers zero question correctly in the last 6 questions is given by:
[tex]\rm P(X=0)=\;^6C_0(0.25)^0(0.75)^{6-0}[/tex]
[tex]\rm P(X=0)=\;^6C_0(0.75)^{6}[/tex]
P(X = 0) = 0.17797
Step 5 - So, the probability that the answers fewer than 2 questions correctly in the last 6 questions is:
[tex]\rm P = P(X=0)+P(X=1)[/tex]
P = 0.17797 + 0.35595
P = 0.53392
P = 53.392%
For more information, refer to the link given below:
https://brainly.com/question/795909
