Chapter Closure
Sign In
Three combinations result in you getting thrown in the pool. To calculate the risk of getting these combinations, we have to consider the probability of spinning each field.
From the diagrams we see that one sector occupies a right angle. This means the last sector must occupy a 270^(∘) angle. With this information we can figure out the ratio that each sector occupies of the spinner.
In Spinner B, each sector occupies a third of the circle. Therefore, the probability of getting any sector on the second spinner is 13.
The probability of two independent events occurring is the product of the event's probabilities. P(1,5): 3/4* 1/3= 3/12 [0.8em] P(1,7): 3/4* 1/3= 3/12 [0.8em] P(3,5): 1/4* 1/3= 1/12 Finally, we will add these probabilities to get the union of all combinations that results in you getting thrown in the pool. P(thrown in the pool) [-0.8em] 3/12+ 3/12+ 1/12=7/12
In Spinner C, each sector occupies a quarter of the circle. Therefore, the probability of getting any of the sectors on the second spinner is 14.
In Spinner D, each field occupies a third of the circle. Therefore, the probability of getting any of the fields on the second spinner is 13.
Again, the probability of two independent events happening is the product of these individual probabilities. In this case, though, we might want to calculate the probability of not getting thrown in the pool, as it involves less calculations. We can find the complement to this. P(4,6): 1/4* 1/3= 1/12 [0.8em] P(5,5): 1/4* 1/3= 1/12 [0.8em] P(5,6): 1/4* 1/3= 1/12 Finally, we will add these probabilities to get the union of all combinations that leads to not getting thrown in the pool and subtract the result from 1. P(thrown in the pool) [-0.8em] 1- ( 1/12+ 1/12+ 1/12)=9/12