the relative frequency table shows the results of a survey in which parents were asked how much time their…

the relative frequency table shows the results of a survey in which parents were asked how much time their children spend playing outside and how much time they spend using electronics.\n\ntime spent by children\n| |at least 1 hr/day using electronics|less than 1 hr/day using electronics|total|\n|--|--|--|--|\n|at least 1 hr/day outside|2|14|16|\n|less than 1 hr/day outside|42|6|48|\n|total|44|20|64|\n\ngiven that a child spends at least 1 hour per day outside, what is the probability, rounded to the nearest hundredth if necessary, that the child spends less than 1 hour per day on electronics?\n0.22\n0.25\n0.70\n0.88

the relative frequency table shows the results of a survey in which parents were asked how much time their children spend playing outside and how much time they spend using electronics.\n\ntime spent by children\n| |at least 1 hr/day using electronics|less than 1 hr/day using electronics|total|\n|--|--|--|--|\n|at least 1 hr/day outside|2|14|16|\n|less than 1 hr/day outside|42|6|48|\n|total|44|20|64|\n\ngiven that a child spends at least 1 hour per day outside, what is the probability, rounded to the nearest hundredth if necessary, that the child spends less than 1 hour per day on electronics?\n0.22\n0.25\n0.70\n0.88

Answer

Explanation:

Step1: Identify relevant values

We want the probability that a child spends less than 1 - hr/day on electronics given they spend at least 1 - hr/day outside. The number of children who spend at least 1 - hr/day outside and less than 1 - hr/day on electronics is 14, and the total number of children who spend at least 1 - hr/day outside is 16.

Step2: Calculate conditional - probability

The formula for conditional probability $P(A|B)=\frac{P(A\cap B)}{P(B)}$. In terms of frequencies, if $A$ is the event of spending less than 1 - hr/day on electronics and $B$ is the event of spending at least 1 - hr/day outside, then the probability is $\frac{\text{Number of }A\cap B}{\text{Number of }B}$. So the probability $P=\frac{14}{16}$.

Step3: Simplify the fraction

$\frac{14}{16}=\frac{7}{8}=0.875\approx0.88$.

Answer:

0.88