7.12.5: Chapter Test

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    From LibreTexts, under CC BY 4.0, as the source states it; its equations are written in TeX, which the PDF shows typeset. This page at LibreTexts.

    Each of the following exercises involve drawing a Scrabble tile from a bag. These tiles are labeled with a letter and a point value, as follows: A(1), C(3), D(2), E(1), E(1), J(8), K(5), O(1), R(1), R(1).
    Exercise \(\PageIndex{1}\)

    How many ways are there to draw a vowel and then a consonant from the bag?

    Exercise \(\PageIndex{2}\)

    How many ways are there to draw a tile worth an even number of points and then a tile worth an odd number of points from the bag?

    Exercise \(\PageIndex{3}\)

    How many ways are there to draw 4 tiles from the bag without replacement, if order matters?

    Exercise \(\PageIndex{4}\)

    How many ways are there to draw 4 consonants from the bag without replacement, if order matter?

    Exercise \(\PageIndex{5}\)

    How many ways are there to draw 4 tiles from the bag with replacement, if order does not matter?

    Exercise \(\PageIndex{6}\)

    How many ways are there to draw 4 consonants from the bag with replacement, if order does not matter?

    Exercise \(\PageIndex{7}\)

    Give the sample space of the experiment that asks you to draw 2 tiles from the bag with replacement and note their point values, where order doesn’t matter. Give the outcomes as ordered pairs.

    Exercise \(\PageIndex{8}\)

    Give the sample space of the experiment that asks you to draw 2 tiles from the bag with replacement and note their point values, where order doesn’t matter. Give the outcomes as ordered pairs.

    Exercise \(\PageIndex{9}\)

    If you draw a single tile from the bag, what is the probability that it’s an E?

    Exercise \(\PageIndex{10}\)

    If you draw a single tile from the bag, what is the probability that it’s not an A?

    Exercise \(\PageIndex{11}\)

    If you draw 3 tiles from the bag without replacement, what is the probability that they spell RED, in order?

    Exercise \(\PageIndex{12}\)

    If you draw 3 tiles from the bag without replacement, what is the probability that they spell RED, in any order?

    Exercise \(\PageIndex{13}\)

    What are the odds against drawing a vowel?

    Exercise \(\PageIndex{14}\)

    Use your answer to question 12 to find the odds against drawing three tiles without replacement and being able to spell RED.

    Exercise \(\PageIndex{15}\)

    If you draw one tile, what is the probability of drawing a J or a K?

    Exercise \(\PageIndex{16}\)

    If you draw one tile, what is the probability that it’s a vowel or that it’s worth more than 4 points?

    Exercise \(\PageIndex{17}\)

    Suppose you’re about to draw one tile from the bag. Find \(P({\text{the letter is R}})\) and \(P({\text{the letter is R}}|{\text{the point value is 1}})\).

    Exercise \(\PageIndex{18}\)

    If you draw 2 tiles with replacement, what is the probability of drawing a consonant first and then a vowel?

    Exercise \(\PageIndex{19}\)

    If you draw 2 tiles without replacement, what is the probability of drawing a consonant first and then a vowel?

    Exercise \(\PageIndex{20}\)

    If you draw 10 tiles with replacement, what is the probability that you draw exactly 3 vowels? Round to 3 decimal places.

    Exercise \(\PageIndex{21}\)

    If you draw 100 tiles with replacement, what is the probability that you draw fewer than 35 vowels? Round to 4 decimal places.

    Exercise \(\PageIndex{22}\)

    Find and interpret the expected number of points on the tile, assuming you draw 1 tile from the bag.

    Exercise \(\PageIndex{23}\)

    Find the expected sum of points on 2 tiles, selected without replacement.

    Exercise \(\PageIndex{24}\)

    If your friend offers you a bet where they pay you $10 if you draw a vowel from the bag, but you owe them $5 if you draw a consonant, should you take it? How do you know?

    This page titled 7.12.5: Chapter Test was last modified on Thu, 02 Jan 2025 09:27:32 GMT and is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by OpenStax via source content that was edited to the style and standards of the LibreTexts platform.