Question

Nathan surveyed the students in his geography class and his algebra class about video games,

B out of the 30 students in his geography class like his favorite video game.
14 out of the 26 students in his algebra class like his favorite video game.
If Nathan randomly selects one student from each class, what is the probability that neither student likes Nathan's favorite video game?
A. 22/65
B. 60/91
C. 4/7
D. 28/105

Answer 1

The probability that neither student likes Nathan's favorite video game is 22/65 (option A), calculated by determining the likelihood that a student in each class does not like the game and multiplying these probabilities.

Step-by-step explanation:

To solve for the probability that neither student likes Nathan's favorite video game, we must first determine the probability that a given student does not like the game in each class. In his geography class, 8 out of 30 students like the video game, which means 22 out of 30 do not. In algebra class, 14 out of 26 like the game, thus 12 out of 26 do not like the video game.

To find the combined probability that one student from each class does not like the game, we multiply the probabilities for each class:

• Probability in geography class = 22/30
• Probability in algebra class = 12/26

Multiplying these probabilities gives us:

(22/30) * (12/26) = (11/15) * (6/13) = 66/195

After simplifying this, we get:

66/195 = 22/65

Therefore, the probability that neither student likes Nathan's favorite video game is 22/65, which corresponds to option A.