One-half of the students at Greendale Middle School take art. Two-thirds of the students take Spanish. Deshawn uses a coin and a standard number cube as a simulation of the students at Greendale Middle School.
Deshawn lets “T” represent a student taking art and “H” represent a student not taking art. He lets the numbers 1, 2, 3, and 4 on the number cube represent a student taking Spanish, and the numbers 5 and 6 represent a student not taking Spanish. The table shows the results of Deshawn’s simulation.
T5
T2
H1
T5
H2
T3
H6
H4
H4
T1
H6
H1
T6
T2
T4
T3
H3
H4
H4
T1
Find the probability that a student at Greendale Middle School takes neither art nor Spanish.
A. Start Fraction 3 over 20 End Fraction
B. two-fifths
C. start fraction 7 over 20 end fraction
D. one-tenth..
To find the probability that a student takes neither art nor Spanish, we need to look for the outcomes that correspond to not taking either subject. From the given chart, the outcomes that represent not taking art are H1, H2, H6, H4, H4, H6, H3, H4, and H4, which have a total frequency of 9. The outcomes that represent not taking Spanish are H1, H2, H6, H6, H4, H4, H3, H4, and H4, which also have a total frequency of 9. Out of the total of 20 outcomes, the 9 outcomes that correspond to not taking either subject are counted twice, so we need to subtract them once to avoid overcounting. Therefore, the probability of a student not taking either art or Spanish is:
(20 - 9) / 20 = 11/20
Answer: C. start fraction 7 over 20 end fraction
To find the probability that a student at Greendale Middle School takes neither art nor Spanish, we need to count the number of outcomes where a student is not taking art or Spanish and divide it by the total number of outcomes.
Looking at the table, the outcomes where a student is not taking art or Spanish are represented by "H" for not taking art and the numbers 5 and 6 on the number cube for not taking Spanish. Counting these outcomes, we have:
H5
H1
H6
H4
H4
H6
H1
H6
There are 8 outcomes where a student is not taking art or Spanish.
The total number of outcomes is the total number of entries in the table, which is 20.
So, the probability that a student at Greendale Middle School takes neither art nor Spanish is 8/20, which simplifies to 2/5.
Therefore, the answer is B. two-fifths.