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

a science teacher presented a balloon to her class, and posed the question, \if i keep this balloon in the freezer overnight, what will occur?\ she followed up with, \how certain are you of your answer?\ the teacher recorded her students responses. certain uncertain shrink 4 6 stay the same 6 3 expand 3 2 what is the probability that a randomly selected student was uncertain given that the student believes the balloon will shrink? simplify any fractions.

a science teacher presented a balloon to her class, and posed the question, \if i keep this balloon in the freezer overnight, what will occur?\ she followed up with, \how certain are you of your answer?\ the teacher recorded her students responses. certain uncertain shrink 4 6 stay the same 6 3 expand 3 2 what is the probability that a randomly selected student was uncertain given that the student believes the balloon will shrink? simplify any fractions.

Answer

Explanation:

Step1: Identify relevant values

We want P(Uncertain | Shrink). The number of students who think it will shrink and are uncertain is 6, and the total number of students who think it will shrink is (4 + 6=10).

Step2: Calculate conditional - probability

The formula for conditional probability (P(A|B)=\frac{P(A\cap B)}{P(B)}). In terms of counts, (P(Uncertain | Shrink)=\frac{\text{Number of uncertain and shrink}}{\text{Number of shrink}}). So (P(Uncertain | Shrink)=\frac{6}{10}=\frac{3}{5}).

Answer:

(\frac{3}{5})