MATH SOLVE

3 months ago

Q:
# An amusement park reports that the probability of a visitor riding its largest roller coaster is 30 percent, the probability of a visitor riding its smallest roller coaster is 20 percent, and the probability of a visitor riding both roller coasters is 15 percent.Which equation can be used to calculate the probability of a visitor riding the largest or the smallest roller coaster?

Accepted Solution

A:

Answer:The equation is P(L or S) = 0.3 + 0.2 - 0.15Step-by-step explanation:* Lets study the meaning of "or" , "and" on probability
- The use of the word "or" means that you are calculating the probability that either event A or event B happened
- Both events do not have to happen
- The use the word "and" means that both event A and B have to happen
* The addition rules are:
# P(A or B) = P(A) + P(B) ⇒ mutually exclusive (events cannot happen
at the same time)
# P(A or B) = P(A) + P(B) - P(A and B) ⇒ non-mutually exclusive (if they have at least one outcome in common)
- The union is written as "A∪B" or "A or B" - The Both is written as "A∩B" or "A and B"
* Lets solve the question
- The probability P(L) of a visitor riding its largest roller coaster is 30%∵ P(L) = 30% = 30/100 = 0.3
- The probability P(S) of a visitor riding its smallest roller coaster is 20%∵ P(S) = 20% = 20/100 = 0.2
- The probability of a visitor riding both roller coasters is 15%∵ P(L and S) = 15% = 15/100 = 0.15- To find P(L or S) lets use the rule of non-mutually exclusive
∵ P(A or B) = P(A) + P(B) - P(A and B)
∴ P(L or S) = P(L) + P(S) - P(L and S)
- Substitute the values above to find the probability of a visitor riding the largest or the smallest roller coaster∴ P(L or S) = 0.3 + 0.2 - 0.15 = 0.35∴ The probability of a visitor riding the largest or the smallest roller coaster is 0.35* The equation is P(L or S) = 0.3 + 0.2 - 0.15