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# Tenth Grade (Grade 10) Statistics and Probability Concepts Questions

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Grade 10 Represent and Determine Probability CCSS: HSS-CP.B.7
Jason and Eva are watching their friends play poker. They can see Josh's cards. Josh currently has four cards in his hand, and is about to receive his fifth and final card. He has the ace of clubs, two of clubs, three of clubs, and four of clubs. Jason and Eva agree that the best options for his next card would be the five of clubs, or any card in the clubs suit. Jason says that the probability of getting the five of clubs or any remaining club card is the same as simply the probability of getting any remaining club card. Eva disagrees, saying that the probability of simply getting any remaining club card would be different than the probability of getting any remaining club card or the five of clubs. Who is correct and why?
1. Eva is correct, because the probability of the two events must be added together, which will be higher than the probability of either event by itself since both of these events have a probability greater than zero.
2. Eva is correct, since when using the addition rule of probability, one must always add the two probabilities (in this case choosing the five of clubs and then choosing any remaining club card), and then subtract the probability that both events occur.
3. Jason is correct, because the probability of choosing the five of clubs AND any remaining club card is equal to the probability of choosing the five of clubs. Using the addition rule, these cancel out and one is left with the probability of choosing any remaining club card.
4. Jason is correct, since the probability of choosing the five of clubs is so low, that it can be ignored.
Grade 10 Collecting and Interpreting Data CCSS: HSS-CP.A.1
Find $A nn B nn C$ if $A = {2,4,6,8,10}, \ \ B = {1,2,3,4,5,6}$, and $C = {2,6,10,14}$.
1. $emptyset$
2. ${2,4,6,10}$
3. ${1,2,3,4,5,6,8,10,14}$
4. ${2,6}$
Grade 10 Represent and Determine Probability CCSS: HSS-CP.B.7
Grade 10 Bar Graphs
Which type of graph would you use to show the populations of five neighboring countries?
1. Circle/pie graph
2. Line graph
3. Scatter plot graph
4. Bar graph
Grade 10 Represent and Determine Probability CCSS: HSS-CP.A.1, HSS-CP.A.2
Grade 10 Represent and Determine Probability CCSS: HSS-CP.A.3
Mary is doing an experiment where she chooses two marbles, one after the other without replacement, from a bag of marbles. The bag of consists of 5 green, 6 red, and 9 blue marbles. She wants to find the probability that she chooses a blue marble given that she chose a green marble first. She lets G be the event that she chooses a green marble and B be the event that she chooses a blue marble. Mary reasons that, since $P(G) = 1/4$ and $P(B) = 9/20$, $P(G " then " B) = 9/80$. (She uses "then" instead of "and" because the events happen one after the other). Therefore, she determines that $P(B|G) = 9/20$. Is she correct, and why?
1. Yes, her assumptions and steps are all correct.
2. No, she assumed that G and B are independent when they are not. $P(G " then " B) = 9/76$, and therefore $P(B|G) = 9/19$.
3. No, she calculated P(G then B) incorrectly. $P(G " then " B) = 14/20 = 7/10$, and therefore $P(B|G) = 14/5$.
4. No, she found $P(G " then " B)$, when this is unnecessary. Since the events are independent, she can simply say $P(G) = P(G|B)$.
Grade 10 Represent and Determine Probability CCSS: HSS-CP.A.1
The probability of an event occurring is $6/15$. What is the probability of the complement?
1. $3/5$
2. $4/5$
3. $5/3$
4. $15/6$
Grade 10 Collecting and Interpreting Data CCSS: HSS-CP.A.1
Given $A = {1,2,3,4,5}, \ \ B = {4,5,6,7,8}, \ \ C = {6,7,8,9,10}$, find $A uu B uu C$.
1. ${1,2,3,4,5,6,7,8,9,10}$
2. $emptyset$
3. ${4,5,6,7,8}$
4. ${1,2,3,9,10}$
Grade 10 Represent and Determine Probability CCSS: HSS-CP.A.1
Pedro needs a 2 on the roll of a die in order to win a game. What is his probability of failure?
1. $0$
2. $1/6$
3. $5/6$
4. $1$
Grade 10 Represent and Determine Probability
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