# PROBABILITY CALCULATIONS

A) The Ludlow Wildcats baseball team, a minor league team in the Cleveland Indians orgainzation, plays 70 precent of their games at night and 30 percent during the day. The team wins 50 percent of their night games and 90 percent of their day games. According to today's newspaper, they won yesterday. What is the probability the game was played at night?

b) With each purchase of a large pizza at Tony's Pizza, the customer receives a coupon that can be scratched to see if a prize will be awarded. The odds of winning a free soft drink are 1 in 10, and the odds of winning a free large pizza are 1 in 50. You plan to eat lunch tomorrow at Tony's. What is the probability:

1. That you will win either a large pizza or a soft drink

2. That you will not win a prize?

3. That you willn ot win a prize on three consecutive visits to Tony's

4. That you will win at least one prize on one of your next three visits to Tony's

c) There are four people being considered for the position of chief executive officer of Dalton Enterprises. Three of the applicants are over 60 years of age. Two are female, of which only one is over 60.

1) What is the probability that a candidate is over 60 and female

2. Given that the candidate is male, what is the probability he is less than 60

3) Givn that the person is over 60, what is the probability the person is female

#### Solution Preview

a) The Ludlow Wildcats baseball team, a minor league team in the Cleveland Indians organization, plays 70 percent of their games at night and 30 percent during the day. The team wins 50 percent of their night games and 90 percent of their day games. According to today's newspaper, they won yesterday. What is the probability the game was played at night?

% of games played at night = 70%

% of games played during day = 30%

% of night games won =50%

% of day games won= 90%

Probability of winning

= Probability of winning at night + Probability of winning during day

= % of games played at night x % of night games won + % of games played during day x % of day games won

= 70% x 50% + 30% x 90%

= 0.35 + 0.27 = 0.62

Probability that the game was played during night given that the game was won

= Probability of winning at night / Probability of winning

= 0.35 / 0.62 = 35/62

Answer: Probability = 35/62

This can be understood in a different way

Let the number of games played be 100

Out of these 100 games, 70 games were played at night and 30 during day

Out of 70 games played at night no of games won = 50% x 70 = 35 games and the number of games lost = 50% x 70 ...

#### Solution Summary

Answers 3 questions on probability calculations.