Probability

Make a Prediction

100

Karina rolled a standard die 57 times during one of her math stations.  How many times could Katrina predict rolling a 2 or a 6?

19 times

200

A basketball player made 12 free throws in his last 36 attempts.  How many free throws would the basketball player be expected to make in 78 attempts?

26

300

A school counselor surveyed 90 randomly selected students about the languages they speak. Of the students surveyed, 16 speak more than one language fluently. Based on these results, how many of the 1,800 students at the school can be expected to speak more than one language fluently?

320

400

A random survey of 75 eighth graders at Cedar Middle School showed that 37 of them do volunteer work. Use these results to predict the approximate number of students who do volunteer work out of the 500 eighth graders at the school.

247

500

A principal randomly chose 40 students from grade 5. Of these students, 9 were wearing watches. Based on this information, what is the most reasonable prediction of the number of students NOT wearing watches in a group of 120 students from grade 5?

93

Dependent Events

100

Please define what a Dependent Event is?

What is two events are dependent if the outcome or occurrence of the first affects the outcome of the second so that the probability is changed.

200

Give an example of a Dependent Event.

What is 1) If we wake up late, we will be late to office. 2) If it rains, we use an umbrella.

300

True of false if you see a problem and it says it is without replacement is it a dependent event why?

Yes, it is a dependent event because with out replacement affects the probability.

400

In a pack of 52 cards, 4 of the cards are Kings. Two cards are randomly picked from the pack. Find the probability of picking: a) a ten and a jack without replacement

What is 4/663 P(10) x P(jack) 4/52 x 4/51 = 16/2652 reduces to 4/663

500

Arthur has 4 brown, 5 violet, and 3 pink sweaters. If he selects 2 sweaters one after the other without replacement, then what is the probability that both are violet in color?

What is 5/33 P(violet) x p(violet 2nd draw) 5/14 x 4/11 = 20/132 divide by 4 and get 5/33

Independent Events

100

Define what an Independent Event is?

What is two events, A and B are independent if the fact that A occurs does not affect the probability.

200

Give an example of an Independent Event.

You toss a coin than toss another coin.

300

Find the probability of getting a 5 on a number cube and tails on the dime.

What is 1/12 5 on dice * tails 1/6 * 1/2 = 1/12

400

What is the probability of a quarter being heads tossed 7 times?

What is 1/128 1/2*1/2*1/2*1/2*1/2*1/2*1/2 =1/128

500

A box contains 6 red marbles, 4 blue marbles, and 8 yellow marbles. Find the probability of yellow and red if a marble is selected and replaced, and then a second one drawn.

What is 4/27 Red x yellow 8/18 x 6/18 = 48/324 reduces to 4/27

Independent and Dependent Events

100

You flip a coin and roll a six-sided die. What is the probability of flipping a head and rolling a 3?

What is 1/12? Explanation: Heads 3 on die Event A x Event B 1/2 x 1/6 = 1/12

200

You have a deck of 8 red cards and 7 blue cards. What is the probability of selecting a red card, not replacing it, and then picking another red card?

What is 28/105 Explanation: P(red 1st draw) x P(red 2nd draw ) 8/15 x 7/14 = 56/210 Reduces to 28/105

300

A drawer contains 3 red paperclips, 4 green paperclips, and 5 blue paperclips. One paperclip is taken from the drawer and is NOT replaced. Another paperclip is taken from the drawer. What is the probability that the first paperclip is red and the second paperclip is blue?

What is 5/44 Explanation: Because the first paper clip is NOT replaced, the sample space of the second event is changed. The sample space of the first event is 12 paperclips, but the sample space of the second event is now 11 paperclips. The events are dependent. P(red then blue) = P(red) • P(blue) = 3/12 • 5/11 = 15/132 = 5/44.

400

A box contains 3 red marbles, 6 blue marbles, and 1 white marble. The marbles are selected at random, one at a time, and are not replaced. Find the probability of a white draw than a blue marble.

What is 1/15 Explanation: White Marble 1/10 Blue Marble choose without replacement 6/9 P(W) x P(B) 1/10 x 6/9 = 6/90 reduces to 1/15

500

A box contains 3 red marbles, 6 blue marbles, and 1 white marble. The marbles are selected at random, one at a time, and are not replaced. Find the probability of a red, red and blue.

What is 1/20 Explanation: Red 3/10 Red 2/9 Blue 6/8 P(Red) x P(Red) x P(Blue) 3/10 x 2/9 x 6/8 = 36/720 reduces to 1/20

Random

100

A spinner is divided into 6 equal sections: red, blue, orange, green, yellow, and purple. What is the probability of spinning a green or a yellow?

What is 1/3?

200

Using a six-sided die, what is the probability of rolling an odd number or a 4?

What is 2/3?

300

Using a 12-sided die, what is the probability of rolling an even number or an odd number?

What is 1?

400

Ray owns a bakery.  At the end of the day he bags up his leftover cookies and takes them to a food pantry.  Today he had 4 chocolate chip cookies, 2 white chocolate cookies, 3 pecan pie cookies, 2 peanut butter cookies, and 1 piece of fudge.  What is the probability a bag will have a chocolate chip cookie if Ray puts one cookie in each bag?

1/3

500

A popular game involves rolling five dice. Points are given based on the numbers that are rolled on each one. A player earns a 100 point bonus if the same number is rolled on each one. What is the probability that all five will be the same on a single roll?

1/7,776