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.\n| |certain|uncertain|\n|--|--|--|--|\n|shrink|4|6|\n|stay the same|6|3|\n|expand|3|2|\nwhat is the probability that a randomly selected student was uncertain given that the student believes the balloon will shrink?\nsimplify 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.\n| |certain|uncertain|\n|--|--|--|--|\n|shrink|4|6|\n|stay the same|6|3|\n|expand|3|2|\nwhat is the probability that a randomly selected student was uncertain given that the student believes the balloon will shrink?\nsimplify any fractions.

Answer

Explanation:

Step1: Find total students who believe balloon will shrink

Add the number of certain and uncertain students who believe the balloon will shrink. $4 + 6=10$.

Step2: Calculate the conditional - probability

The number of uncertain students who believe the balloon will shrink is 6. The formula for conditional probability $P(A|B)=\frac{n(A\cap B)}{n(B)}$. Here, $A$ is the event of being uncertain and $B$ is the event of believing the balloon will shrink. So the probability is $\frac{6}{10}=\frac{3}{5}$.

Answer:

$\frac{3}{5}$