Lingo
In the gameshow Lingo, the team that correctly guesses a mystery word gets a chance to pull two Lingo balls from a bin. Balls in the bin are labeled with numbers that match the numbers still on the team's Lingo board. There are also three prize balls and three red "stopper" balls in the bin. If a stopper ball is drawn first, the team loses its second draw. To form a Lingo, the team needs five numbers in a row—vertically, horizontally, or diagonally. Consider the sample Lingo board below for a team that has just guessed a mystery word.

a. What is the probability that the first ball selected is on the Lingo board?

Suppose you live in a town with two hospitals—one large and the other small. On a given day in one of the hospitals, 60% of the babies who were born were girls. Which one do you think it is? Or, is it impossible to tell. Support your decision?

If events E and F are disjoint and the events F and G are disjoint, must the events E and G necessarily be disjoint? Give an example to illustrate your opinion.

Text Twist

In the game Text Twist, six letters are given and the player must form words of different lengths using those letters. Suppose the letters in a particular game are ENHSIC.

c. The solution to this game has three 6-letter words. To move to the next round, the player must get at least one of the six-letter words. If the player simply guesses, what is the probability of getting one of the six-letter words on the first try?

Lingo

In the gameshow Lingo, the team that correctly guesses a mystery word gets a chance to pull two Lingo balls from a bin. Balls in the bin are labeled with numbers that match the numbers still on the team's Lingo board. There are also three prize balls and three red "stopper" balls in the bin. If a stopper ball is drawn first, the team loses its second draw. To form a Lingo, the team needs five numbers in a row—vertically, horizontally, or diagonally. Consider the sample Lingo board below for a team that has just guessed a mystery word.

c. What is the probability that the team makes a Lingo on their first draw?

Roulette

In the game of roulette, the wheel has 38 slots numbered 0, 00, 1, 2, …, 36. A metal ball is spun around the wheel and can land in any of the slots. The slots numbered 0 and 00 are green, the odd numbers are red, and the even numbers are black..

d. Determine the probability that the metal ball lands in both the number 31 slot and a black slot at the same time. What term is used to describe this event?

Long Life? In a poll conducted by Genworth Financial, a random sample of adults was asked, “What age would you like to live to?” The results of the survey are given in the table.

a. Construct a probability model of the data.

Gestation Period versus Weight The following data represent the birth weights (in grams) of babies born in 2017, along with the period of gestation.

b. What is the probability that a randomly selected baby born in 2017 weighed between 3000 and 3999 grams?