Explanation:

Each of the two coin flips to represent one event. The probability of obtaining exactly one heads and also exactly one tails have the right to be modeled as follows:

Event 1 * event 2

The an essential to knowledge this trouble is to recognize that one of two people heads adhered to by tails, or tails adhered to by heads, would meet the details overall outcome asked for in the problem. Due to the fact that Event 1 will develop either a heads or a tails, we have a 100% possibility of obtaining an end result from occasion 1 that will satisfy one of the two requirements of the certain overall outcome (one heads and also one tails). Occasion 2 will then have actually a 50% chance of producing result that is the opposite, rather than the same, as the outcome of occasion 1. Us can as such calculate the probability of our details overall outcome together follows:

 

100% * 50%

1 * 0.5

0.5 = 50% 

 

Therefore, the probability the obtaining one heads and also one tails from two coin tosses is 50%. 

 

 




You are watching: On a multiple choice test with four possible answers for each question what is the probability

Report an Error

Example concern #61 : Probability


Assume the you guess: v on each concern of a multiple an option test. There room 12 questions and each question has actually 4 possible answers. What is the probability of getting exactly 8 answer correct?


Possible Answers:

0.32


0.000004


0.002


0.0002


Correct answer:

0.002


Explanation:

This difficulty can be solved using the binomial probability equation:

*

*

*

*

*

*

*

*

*

 


Report an Error

Example concern #1 : Binomial theorem


What is the coefficient of 

*
 if the expression 
*
 is expanded?


Possible Answers:

*



*


*


*


Correct answer:


Explanation:

By the Binomial Theorem, if the expression 

*
 is expanded, the result deserve to be defined as

*

If us set 

*
, then the above expression, through slight rearranging, becomes 

*

The coefficient of the 

*
 term is 

*

To find the the coefficient of 

*
, us set 
*
 and evaluate:

*


Report one Error

Example question #61 : Probability


What is the coefficient of 

*
 in the polynomial
*
 


Possible Answers:
Correct answer:

*


Explanation:

The binomial theorem says that we deserve to represent the polynomial 

*
 as a sum 

*

Thus, if we want to discover the coefficient that

*
,

*
 since
*
,

*
 and
*
.

Therefore the coefficient of

*
 is

*


Report one Error

Example concern #1 : Binomial theorem


You"re taking a multiple selection quiz that has actually

*
 questions. If each question has actually
*
 choices and also you guess on every one of them, what is the probability of getting precisely
*
 questions correct?


Possible Answers:


See more: Which Is True About Supporting Details? ? Which Is True About Supporting Details

Correct answer:

*


Explanation:

This inquiry requires the applications of the binomial theorem because that probability. In bespeak to recognize the probability the getting exactly 6 inquiries right, we should remember the formula because that this theorem:

*

Where

*
is the variety of trials (total questions),
*
is the variety of successes (correct answers),
*
is the probability that success in one attempt (chance of comment a inquiry correctly),
*
is the probability of fail in one psychological (chance of answering a inquiry incorrectly), and also
*
is the probability of getting
*
questions correct out of
*
total questions. Because there space 5 selections for every question, the opportunities of comment a question appropriately are 1/5, or 0.2, and also therefore the opportunities of comment a question erroneously are 4/5, or 0.8. Currently we have all of our values and also can plug them into the formula:

*

The first part that the formula in which we have actually a 10 end a 6 in parentheses method we execute the following calculation: