Determine whether events A and B are independent or not. Circle the best choice.

Question

Determine whether events A and B are independent or not. Circle the best choice. a) A JC student is chosen at random. Event A: The student was born on a Sunday; Event 8: The student's mother was born on a Sunday. Independent Dependent b) A JC student is chosen at random. Event A: The student is average height; Event B: The student's mother is average height. Independent Dependent During a stretch of the 2009 baseball season. Colorado Rockies pitcher Ubaldo Jimenez threw 2825 pitches. Of these 1912 were fastballs, 228 were curveballs, 457 were sliders, and 228 were changeups. For a), suppose that Ubaldo Jimanez is going to throw one pitch. a) What is the probability that he throws a "breaking ball" (i.e.. a curveball or a slider)? For b)-c), suppose that Ubaldo Jimanez is going to throw three independent pitches in a row. b) What is the probability that he throws three fastballs in a row? c) What is the probability that he throws first a fastball, then a slider, then a changeup? d) Explain why Ubaldo Jimanez' three pitches are likely not independent in the context of the situation.

Explanation / Answer

(1a) Independents

(1b)Independents

(2)(a) probability of breaking ball=P(breaking ball)=P(curve ball or slider)=(228+457)/2825=0.2425

(2b)P(fastball)=1912/2825=0.6768

P(3 consecutive fast ball)=0.6768*0.6768*0.6768=0.31

(3c)P(fastball)=1912/2825=0.6768

P(slider)=457/2825=0.1618

P(changeup)=228/2825=0.0807

required probability P(fast ,slider ,changeup)=0.6768*0.1618*0.0807=0.0088

(3d) because next ball will depend on previous ball

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