Class Activity 2
Probability Problems A –answers
1. Barry Bonds Probability of a Home Run.
In the 2001 season, Barry Bonds hit 73 home runs in 476 times. Therefore,
73
P(home run) =
=0.15336
476
567
From his 567 career home runs in 7932 “at bats” , P(home run) =
=0.0.07148
7932
His 2001 record is very different from his career home run record.
2. Probability of a birthday.
The National Statistics Day in Japan is October 18. What is the probability that a person selected
at random has a birthday on October 18?
1
P(birthday on October 180=
(ignoring a leap year)
365
What is the probability that a person selected at random at a birthday in October?
31
P(birthday in October) =
(ignoring a leap year)
365
What is the probability that a person was born on a day of the week that ends with the letter y?
P(birthday in a day of the week that ends in y) = 1
Problem 3. Finding odds in roulette.
A roulette has 38 slots, 0, 00 and the numbers 1 to 36.
Placing a bet on the 18 odd numbers: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35
There are 20 non-odd numbers: 0, 00, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36
What is the probability of winning?
18
P( winning ) 
 0.474
38
What are the actual odds against winning?
There are 18 numbers for winning and 20 against winning, therefore the odds against winning is
20 to 18 (or 10:9)
If the payoff odds are 1:1 and you bet $18, then you make a profit of $18.
If the payoff odds are the same as the odds against winning, that is 20:18, and you bet $18 then
you make a profit of $20
4. Contingency table for the sinking of the Titanic.
Men
Women
Boys
Girls
TOTAL
Survived
332
318
29
27
706
Died
1360
104
35
18
1517
TOTAL
1692
422
64
45
2223
If one of the Titanic passengers is randomly selected, find the probability of getting someone who is a
woman or child.
422
64
45
531
P(woman or child)  P(woman or boy or girl) 



 02389
2223 2223 2223 2223
1692 2223 1692
531
or by the low of complement ation  1  P(man )  1 



 02389
2223 2223 2223 2223
If one of the Titanic passengers is randomly selected, find the probability of getting a man or
someone who survived the sinking.
P(man or survived)  P(man)  P(survived ) - P(man and survived)

1692 706
332
2066



 0.9293
2223 2223 2223 2223
If one of the Titanic passengers is randomly selected, find the probability of getting a woman or
someone who did not survived the sinking.
P(woman or died)  P(woman  P(died) - P(woman and died)

422 1517 104 1835



 0.8255
2223 2223 2223 2223
If we randomly select someone who was aboard the Titanic, what is the probability of getting a man,
given that the selected person died?
This is a conditional probability and the reduced sample space consists of those 1517 who died.
1360
P(man given those who died)  P(man | Died) 
 0.8965
1517
If we randomly select someone who died, what is the probability of getting a man?
1360
P(man given those who died)  P(man | Died) 
 0.8965
1517
What is the probability of getting a boy or girl, given that the randomly selected person is someone
who survived?
29  27 56
P(boy or girl given someone who survided)  P(boy or girld | survived) 

 0.0793
706
706
What is the probability of getting a man or a woman, given that the randomly selected person is
someone who died?
1360  104 1464
P(man or woman given someone who died)  P(man or woman | died) 

 0.9651
1517
1517