A Gallup Poll (June 11-17, 2001) interviewed a random sample of 1094 adults (18

Question

A Gallup Poll (June 11-17, 2001) interviewed a random sample of 1094 adults (18 years or older). The people in the sample were asked how they would rate economic conditions in the United States today. Here are the results. These proportions are probabilities for the random phenomenon of choosing an adult at random and asking the person's opinion on current economic conditions. (a) What must be the probability that the person chosen says "fair"? (b) The official press release focused on the percent of adults giving the economy a "positive" rating where positive is defined as "good" or "excellent."What is this probability? You read in a book on poker that the probability of being dealt three of a kind in a five-card poker hand is 1/50. Explain in simple language what this means. Every fiftieth hand is a three of a kind. Within every fifty hands, there is one three of a kind. You would see three of a kind every 50 hands over the long run.

Explanation / Answer

(a) All probabilites must have sum equal to 1.

so P(Excellent) + P(Good) + P(fair) + P(Poor) + P(No opinion) = 1

0.04 + 0.28 + P(fair) + 0.17 + 0.04 = 1

P(fair ) = 1- 0.53 = 0.47

so P(fair) = 0.47

(b) Pr(Positive) = Pr(good) + Pr( Excellent) = 0.04 + 0.28 = 0.32

so there is 0.32 probability to have an excellent rating.

Q.5 Poker question

Here probability of being dealt three of a kindin a five card poker hand = 1/50

so option (b) is correct that within every fifty hands, there is one three of a kind.

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