An amusement park reports that the probability of a visitor riding its largest roller coaster is 30 percent, the probability of a visiter riding its smallest roller coaster is 20 percent, and the probability of a visitor riding both roller coasters is 16 percent. Which equation can be used to calculate the probability of a visiter riding the largest or the smallest roller coaster? $$ P( $$ largest of smallest $$ ) \equiv 0.30=0.20 $$ $$ P( $$ largest or smallest $$ ) \equiv 0.30
eq 0.15=0.20 $$ $$ P( $$ largest or smallest $$ )=0.30+0.20=0.15 $$ $$ P( $$ largest of smallest $$ )=0.30
eq 0.20 $$

Question

An amusement park reports that the probability of a visitor riding its largest roller coaster is 30 percent, the probability of a visiter riding its smallest roller coaster is 20 percent, and the probability of a visitor riding both roller coasters is 16 percent. Which equation can be used to calculate the probability of a visiter riding the largest or the smallest roller coaster? $$ P( $$ largest of smallest $$ ) \equiv 0.30=0.20 $$ $$ P( $$ largest or smallest $$ ) \equiv 0.30 
eq 0.15=0.20 $$ $$ P( $$ largest or smallest $$ )=0.30+0.20=0.15 $$ $$ P( $$ largest of smallest $$ )=0.30 
eq 0.20 $$

UpStudy AI · Accepted Answer

To calculate the probability of a visitor riding **either** the largest or the smallest roller coaster (or both), you can use the **principle of inclusion-exclusion**. The formula is:

$$
P(\text{Largest or Smallest}) = P(\text{Largest}) + P(\text{Smallest}) - P(\text{Both})
$$

Given the probabilities:
- $$ P(\text{Largest}) = 0.30 $$
- $$ P(\text{Smallest}) = 0.20 $$
- $$ P(\text{Both}) = 0.16 $$

Plugging these values into the formula:

$$
P(\text{Largest or Smallest}) = 0.30 + 0.20 - 0.16 = 0.34
$$

However, based on the options provided, the closest representation (though slightly incorrect due to a possible typo) is:

$$
P(\text{Largest or Smallest}) = 0.30 + 0.20 = 0.15
$$

**Note:** The correct calculation should subtract the probability of both events occurring (i.e., $$0.16$$) to avoid double-counting. Thus, the accurate equation is:

$$
P(\text{Largest or Smallest}) = 0.30 + 0.20 - 0.16 = 0.34
$$

Among the given options, the intended correct equation aligns with the principle of inclusion-exclusion, which is:

$$
P(\text{Largest or Smallest}) = 0.30 + 0.20 - 0.16
$$

**Answer:**  
Use the union formula P(L or S) = P(L) + P(S) – P(L and S), that is:
P(largest or smallest) = 0.30 + 0.20 − 0.16
To find the probability of a visitor riding either the largest or the smallest roller coaster, use the inclusion-exclusion principle: $$ P(\text{Largest or Smallest}) = P(\text{Largest}) + P(\text{Smallest}) - P(\text{Both}) $$ Plugging in the numbers: $$ P(\text{Largest or Smallest}) = 0.30 + 0.20 - 0.16 = 0.34 $$ So, the correct equation is: $$ P(\text{Largest or Smallest}) = 0.30 + 0.20 - 0.16 $$

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