a science teacher presented a balloon to his class, and posed the question, \if i keep this balloon in the…

a science teacher presented a balloon to his class, and posed the question, \if i keep this balloon in the freezer overnight, what will occur?\ he followed up with, \how certain are you of your answer?\ the teacher recorded his students responses.\n\n| |certain|uncertain|\n|--|--|--|\n|shrink|7|5|\n|expand|3|4|\n\nwhat is the probability that a randomly selected student believes the balloon will expand or was uncertain?\n\nsimplify any fractions.

a science teacher presented a balloon to his class, and posed the question, \if i keep this balloon in the freezer overnight, what will occur?\ he followed up with, \how certain are you of your answer?\ the teacher recorded his students responses.\n\n| |certain|uncertain|\n|--|--|--|\n|shrink|7|5|\n|expand|3|4|\n\nwhat is the probability that a randomly selected student believes the balloon will expand or was uncertain?\n\nsimplify any fractions.

Answer

Explanation:

Step1: Calculate total number of students

$7 + 5+3 + 4=19$

Step2: Calculate number of students who believe balloon will expand or were uncertain

Number of students who believe balloon will expand is $3 + 4=7$. Number of students who were uncertain is $5 + 4 = 9$. But we double - counted the 4 students who believe it will expand and were uncertain. So the number of students who believe balloon will expand or were uncertain is $(3 + 4)+(5 + 4)-4=12$

Step3: Calculate the probability

Probability $P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}=\frac{12}{19}$

Answer:

$\frac{12}{19}$