### About Probability:

When working with basic probability problems, we will be asked to find the probability for some given event.

Test Objectives

- Demonstrate the ability to solve a probability problem

#1:

Instructions: Find the probability.

a) A coin is flipped five times. What is the probability that the coin lands heads-up every time?

b) A coin is flipped and then a fair six-sided die is rolled. What is the probability that the coin lands tails-up and the die shows an odd number?

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#2:

Instructions: Find the probability.

a) A game show has a spinner that can land in one of four regions: blue, red, yellow, or green. What is the probability of a contestant spinning three times and landing in the blue region each time?

b) Sarah has eight nickels and seven dimes in her coin purse. Sarah randomly picks a coin from her pocket and places it on the kitchen table. She then randomly picks another coin. What is the probability that the first coin is a nickel and the second coin picked is a dime?

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#3:

Instructions: Find the probability.

a) Jessica has a sock drawer that contains two white socks, two brown socks, and four black socks. What is the probability that she can randomly pick two socks and get a matching pair of black socks?

b) There are eleven shirts in Lindsey’s closet, three blue, three green, and five red. She randomly selects one to wear. What is the probability that it is blue or green?

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#4:

Instructions: Find the probability.

a) You roll a fair six-sided die. What is the probability that the die shows an odd number or a number less than three?

b) Thelma’s sports bag contains five yellow jerseys numbered 1 to 5. Her bag also contains four purple jerseys numbered 1 to 4. She randomly picks a jersey. What is the probability that it is yellow or has a number greater than 3?

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#5:

Instructions: Find the probability.

a) A six-sided die is rolled ten times. What is the probability that the die will come up as an even number exactly five times?

b) A biology exam consists of nine true/false questions. Megan forgot to study and guessed randomly on every question. What is the probability that Megan will answer exactly four questions correctly?

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Written Solutions:

#1:

Solutions:

$$a)\hspace{.2em}\frac{1}{32}$$

$$b)\hspace{.2em}\frac{1}{4}$$

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#2:

Solutions:

$$a)\hspace{.2em}\frac{1}{64}$$

$$b)\hspace{.2em}\frac{4}{15}$$

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#3:

Solutions:

$$a)\hspace{.2em}\frac{3}{14}$$

$$b)\hspace{.2em}\frac{6}{11}$$

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#4:

Solutions:

$$a)\hspace{.2em}\frac{2}{3}$$

$$b)\hspace{.2em}\frac{2}{3}$$

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#5:

Solutions:

$$a)\hspace{.2em}\frac{63}{256}$$

$$b)\hspace{.2em}\frac{63}{256}$$