Explanation:

Each that the 2 coin flips represents one event. The probability the obtaining specifically one heads and also exactly one tails have the right to be modeled together follows:

Event 1 * event 2

The an essential to understanding this difficulty is to acknowledge that one of two people heads followed by tails, or tails complied with by heads, would accomplish the particular overall result asked for in the problem. Due to the fact that Event 1 will develop either a top or a tails, we have a 100% opportunity of obtaining an end result from event 1 that will accomplish one the the two requirements of the specific overall outcome (one heads and one tails). Occasion 2 will then have actually a 50% opportunity of producing an outcome that is the opposite, fairly than the same, together the outcome of event 1. We can as such calculate the probability of our certain overall outcome as 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%. 

 

 




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Example inquiry #62 : Probability


Assume that you guess: v on each concern of a multiple selection test. There are 12 questions and each question has 4 feasible answers. What is the probability that getting specifically 8 answers correct?


Possible Answers:

0.000004


0.32


0.002


0.0002


Correct answer:

0.002


Explanation:

This problem can be addressed using the binomial probability equation:

*

*

*

*

*

*

*

*

*

 


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Example concern #63 : Probability


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 characterized as

*

If we set 

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

*

The coefficient the the 

*
 term is 

*

To find the the coefficient of 

*
, we set 
*
 and evaluate:

*


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Example question #64 : Probability


What is the coefficient of 

*
 in the polynomial
*
 


Possible Answers:
Correct answer:

*


Explanation:

The binomial theorem states that we can represent the polynomial 

*
 as a sum 

*

Thus, if we want to discover the coefficient the

*
,

*
 since
*
,

*
 and
*
.

Therefore the coefficient of

*
 is

*


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Example question #65 : Probability


You"re taking a multiple an option quiz that has actually

*
 questions. If every question has actually
*
 choices and also you guess: v on all of them, what is the probability the getting exactly
*
 questions correct?


Possible Answers:


See more: Convert 88 Cm Equals How Many Inches In 88 Cm? Convert 88 Centimeters To Inches

Correct answer:

*


Explanation:

This question requires the application of the binomial theorem for probability. In bespeak to recognize the probability of getting exactly 6 questions right, we must 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 trial (chance of comment a question correctly),
*
is the probability of failure in one attempt (chance of answering a question incorrectly), and
*
is the probability of acquiring
*
questions correct out of
*
complete questions. Due to the fact that there are 5 selections for every question, the possibilities of comment a question appropriately are 1/5, or 0.2, and also therefore the possibilities of comment a question erroneously are 4/5, or 0.8. Now we have every one of our values and can plug them right into the formula:

*

The first part the the formula in which we have a 10 over a 6 in parentheses means we perform the complying with calculation: