Answer:
The probability that a pint selected at random is either sugarless or vanilla is [tex]\frac{13}{18}[/tex] ⇒ 2nd answer
Step-by-step explanation:
If A and B are to events, then
P(A or B) = P(A) + P(B) - P(A and B)
Probability of an event = [tex]\frac{n(event)}{n(total)}[/tex]
∵ There are 900 pints of ice-cream for sale
∴ n(total) = 900
∵ 200 are sugarless
∴ n(sugarless) = 200
- Divide n(sugarless) by n(total) to find P(sugarless)
∴ P(sugarless) = [tex]\frac{200}{900}[/tex]
∴ P(sugarless) = [tex]\frac{2}{9}[/tex]
∵ 500 are vanilla
∴ n(vanilla) = 500
- Divide n(vanilla) by n(total) to find P(sugarless)
∴ P(vanilla) = [tex]\frac{500}{900}[/tex]
∴ P(vanilla) = [tex]\frac{5}{9}[/tex]
∵ There are 50 sugarless vanilla
∴ n(sugarless and vanilla) = 50
- Divide n(sugarless and vanilla) by n(total) to find P(s and v)
∴ P(s and v) = [tex]\frac{50}{900}[/tex]
∴ P(s and v) = [tex]\frac{5}{90}[/tex]
Let us use the rule above to find P(s or v)
∵ P(s or v) = P(s) + P(v) - P(s and v)
∴ P(s or v) = [tex]\frac{2}{9}+\frac{5}{9}-\frac{5}{90}[/tex]
∴ P(s or v) = [tex]\frac{13}{18}[/tex]
∴ P(sugarless or vanilla) is [tex]\frac{13}{18}[/tex]
The probability that a pint selected at random is either sugarless or vanilla is [tex]\frac{13}{18}[/tex]
