Probability - Cards, From Hand, Pick Two Non-Ordered, To Binomial Equation (Level 2)

This math topic focuses on calculating probabilities using binomial notation, specifically targeting scenarios involving drawing cards. Problems require expressing solutions as fractions using binomial coefficients, such as \(\binom{n}{k}\). The problems represent real-life situations, like drawing specific numbers or suits from a deck, and progressing to express the likelihood of these events. This set of exercises is suitable for understanding and applying binomial theorem concepts in probability and statistics.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

Cards, From Hand, Pick Two Non-Ordered, To Binomial Equation

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Calculate the probability of drawing 2 5s. Show as a fraction in binomial (bracket) notation

Probability - Cards, From Hand, Pick Two Non-Ordered, To Binomial Equation Worksheet

Math worksheet on 'Probability - Cards, From Hand, Pick Two Non-Ordered, To Binomial Equation (Level 2)'. Part of a broader unit on 'Probability and Statistics - Permutations and Combinations Calculating - Practice' Learn online: app.mobius.academy/math/units/probability_and_statistics_permutations_and_combinations_calculation_practice/

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Calculate the probability of drawing 2 Diamonds. Show as a fraction in binomial (bracket) notation

a $A LaTex expression showing \frac{{2\choose4}}{{2\choose2}}$

b $A LaTex expression showing \frac{{2\choose3}}{{6\choose3}}$

c $A LaTex expression showing \frac{{2\choose2}}{{4\choose2}}$

d $A LaTex expression showing \frac{{2\choose2}}{{2\choose4}}$

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Calculate the probability of drawing 2 6s. Show as a fraction in binomial (bracket) notation

a $A LaTex expression showing \frac{{2\choose4}}{{2\choose2}}$

b $A LaTex expression showing \frac{{2\choose2}}{{2\choose4}}$

c $A LaTex expression showing \frac{{2\choose2}}{{4\choose2}}$

d $A LaTex expression showing \frac{{4\choose2}}{{2\choose2}}$

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Calculate the probability of drawing 4 Clubs. Show as a fraction in binomial (bracket) notation

a $A LaTex expression showing \frac{{8\choose4}}{{10\choose4}}$

b $A LaTex expression showing \frac{{4\choose6}}{{4\choose4}}$

c $A LaTex expression showing \frac{{5\choose4}}{{8\choose4}}$

d $A LaTex expression showing \frac{{4\choose4}}{{6\choose4}}$

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Calculate the probability of drawing 2 Diamonds. Show as a fraction in binomial (bracket) notation

a $A LaTex expression showing \frac{{2\choose2}}{{7\choose2}}$

b $A LaTex expression showing \frac{{7\choose2}}{{2\choose2}}$

c $A LaTex expression showing \frac{{2\choose7}}{{2\choose2}}$

d $A LaTex expression showing \frac{{4\choose2}}{{9\choose2}}$

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Calculate the probability of drawing 3 Spades. Show as a fraction in binomial (bracket) notation

a $A LaTex expression showing \frac{{3\choose3}}{{8\choose3}}$

b $A LaTex expression showing \frac{{3\choose3}}{{5\choose3}}$

c $A LaTex expression showing \frac{{3\choose3}}{{3\choose5}}$

d $A LaTex expression showing \frac{{6\choose3}}{{8\choose3}}$

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Calculate the probability of drawing 4 9s. Show as a fraction in binomial (bracket) notation

a $A LaTex expression showing \frac{{4\choose6}}{{4\choose4}}$

b $A LaTex expression showing \frac{{4\choose4}}{{6\choose4}}$

c $A LaTex expression showing \frac{{6\choose4}}{{4\choose4}}$

d $A LaTex expression showing \frac{{8\choose4}}{{10\choose4}}$

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Calculate the probability of drawing 2 Aces. Show as a fraction in binomial (bracket) notation

a $A LaTex expression showing \frac{{4\choose2}}{{2\choose2}}$

b $A LaTex expression showing \frac{{2\choose2}}{{4\choose2}}$

c $A LaTex expression showing \frac{{2\choose4}}{{2\choose2}}$

d $A LaTex expression showing \frac{{2\choose2}}{{2\choose4}}$

e $A LaTex expression showing \frac{{4\choose4}}{{7\choose4}}$