SOLUTION: Finite Mathematics: A contestant draws a sequence of three cards, one question per card, and tries to answer the three questions. There are three cards with history questions, s

Question 1158083: Finite Mathematics:
A contestant draws a sequence of three cards, one question per card, and tries to answer the three questions. There are three cards with history questions, six cards with literature questions, and eight cards with science questions. Find the probability of each of the following. (Round your answers to four decimal places.)
(a) the questions are history, literature, and science, in that order
(b) all three are literature questions
(c) the first is science, the second is history, and the third is science
Answer by KMST(5377) (Show Source): You can put this solution on YOUR website!
At first, there is a total of cards to draw from.
After the first card is drawn, there will be cards to draw from.
After the first card and second have been drawn, there will be cards to draw from.

(a) Probability that the questions are history, literature, and science, in that order:

At first,
cards to draw from, including history cards.
The probability that the first card drawn is a history card is
.
After that,
cards to draw the second card from, including all literature cards.
The probability to draw a literature card after having drawn a history card is
.
After that,
cards to draw the third card from, including all science cards.
The probability to draw a science car after having drawn a history card followed by a literature car is

The probability that the questions are history, literature, and science, in that order is
(rounded to four decimal places).

(b) Probability that all three cards drawn are literature questions:

At first,
cards to draw from, including literature cards.
The probability that the first card drawn is a literature card is
.
After that,
cards to draw the second card from, including literature cards.
The probability to draw a second literature card after having drawn a literature card is
.
After that,
cards to draw the third card from, literature cards.
The probability to draw a third literature card after two literature cards is

The probability that all three questions drawn are literature questions is
(rounded to four decimal places).

(c) Probability that the first card drawn is science, the second is history, and the third is science

At first,
cards to draw from, including science cards.
The probability that the first card drawn is a science card is
.
After that,
cards to draw the second card from, including history cards and science cards.
The probability to draw a history card after having drawn a science card is
.
After that,
cards to draw the third card from, including science cards.
The probability to draw a science card after having drawn a science card and a history card is

The probability that the first card drawn is science, the second is history, and the third is science is
(rounded to four decimal places).

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