Question

Suppose there are 6 runners in the finals of a 100 m sprint, Abbie, Becca, Clarice, Danna, Emma, and Francine. Answer each of the following questions.

1. An analyst, Grace, gives Abbie a 12% chance to place first and Becca an 8% chance to place second. Assume these percentages are accurate. Can we determine the probability that Abbie will place first and Becca will place second? Why or why not?

2. Grace further informs us that the two favorites to win the race are Danna and Francine. Grace gives Danna a 48% chance to win the race and Francine a 32% chance to win. Assume these percentages are accurate. Find the probability that Danna or Francine wins the race, if possible. If not possible, explain why.

3. Suppose Abbie places first. Does this mean that Grace's probabilities were wrong? Justify your answer using terms and reasoning discussed in Chapter 5.

Answer 1

1.

Yes, we can find

following is the way :

P( Abbie will place first and Becca will place second )

= P(abbie first) * [P(becca first)/(1 - P(abbie first))]

= 0.12 * [0.08 / (1-0.12)]

= 0.0109

2.

P(danna or francine) = P(danna) + P(francine)

= 0.48+0.32

= 0.80

3.

NO, It doesn't mean that Grace's probabilities were wrong because the probabilities show how much likely is some event to happen

But the outcome can be anything with probibility > 0

here P(abbie wins) = 0.12

P(abbie wins) > 0

therefore it is possible event so we cannot say that Grace's probabilities were wrong

(please UPVOTE)