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N3Race GameIn the race game, the contestant is shown four prizes.they then have 45 seconds to matchthe correct prices to the correct prizes. After placing the prices, the contestants is able todetermine how many of their choices are correct but not which choices are correct. theycan use the remainder of their time to readjust.A) what is the probability that you would guess all four pricescorrectly in only one try?2) Is this an example of an independent or dependentprobability?

Answer :

SOLUTION

Looking at this, we have a total of four prices.

When the first price is picked, the probability becomes

[tex]\frac{1}{4}[/tex]

After the first price is picked, we have 3 prices left. The probability of picking the second becomes

[tex]\frac{1}{3}[/tex]

Probability of picking the 3rd becomes

[tex]\frac{1}{2}[/tex]

Note that this is without replacement, hence the probability of picking the last becomes

[tex]\frac{1}{1}=1[/tex]

So the require probability becomes

[tex]\begin{gathered} \frac{1}{4}\times\frac{1}{3}\times\frac{1}{2}\times1 \\ =\frac{1}{24} \end{gathered}[/tex]

Hence the answer is

[tex]\frac{1}{24}[/tex]

It is a dependable probability because it is a probability without replacement, since the preceding event has an effect on the probability of the next event

Hence the answer is dependable probability

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