MAT exam
List the three basic rules for computing probability - Answer-Empirical Probability
Theoretical Probability
Subjective Probability
State the three probability limits for probability - Answer-1. Probability is between 0 and 1-inclusive
2. The probability of an impossible even is 0
3. The probability of an event that must occur is 1
List the sample space for flipping a coin three times - Answer-HHH, HHT, HTH, HTT
THH, THT, TTH, TTT
total outcomes= 8
If you flip a coin three times, what is the probability of tossing 2 heads and 1 tail? - Answer-HHT, HTH,
THH
P(2heads and 1tail)=3/8
If you flip a coin 4 times, what is the probability of tossing 4 tails? - Answer-
P(T&T&T&T)=1/2x1/2x1/2x1/2= 1/16
What is the probability of getting a 9 when a pair of dice is rolled? - Answer-3-6, 4-5, 5-4, 6-3
P(9)= 4/36=1/9
, A gambler assesses the probability of a win by Slick Joe to be 3/5. According to the gambler, what are
the odds in favor of Slick Joe winning? - Answer-Odds in favor=successes OVER failures
Probability= successes OVER outcomes
5-3=2
Answer is= 3/2
Another gambler assesses the odds against Slick Joe's winning to be 2 to 1. Find the gambler's
assessment of the probability that Slick Joe will win. - Answer-Odds against=failures OVER successes
Odds against= 2/1
2+1=3
P(win)=successes OVER outcomes =1/3
A small box contains twenty marbles. Eight of them are green, seven are red, and five are blue. What is
the probability that you will reach into the box and draw out
A. a blue marble?
B. a green or red marble?
C. If you are going to draw out three marbles, one at a time, and you are not going to replace the
marbles in the box once they are drawn, what is the probability that all three will be blue? - Answer-8
green
7 red
5 blue
total 20
A. P(blue)= 5/20=1/4
B. P(green or red)=8/20+7/20=15/20=3/4
C. P(all blue)=P(B&B&B)=5/20x4/19x3/18=60/6840=1/114
List the three basic rules for computing probability - Answer-Empirical Probability
Theoretical Probability
Subjective Probability
State the three probability limits for probability - Answer-1. Probability is between 0 and 1-inclusive
2. The probability of an impossible even is 0
3. The probability of an event that must occur is 1
List the sample space for flipping a coin three times - Answer-HHH, HHT, HTH, HTT
THH, THT, TTH, TTT
total outcomes= 8
If you flip a coin three times, what is the probability of tossing 2 heads and 1 tail? - Answer-HHT, HTH,
THH
P(2heads and 1tail)=3/8
If you flip a coin 4 times, what is the probability of tossing 4 tails? - Answer-
P(T&T&T&T)=1/2x1/2x1/2x1/2= 1/16
What is the probability of getting a 9 when a pair of dice is rolled? - Answer-3-6, 4-5, 5-4, 6-3
P(9)= 4/36=1/9
, A gambler assesses the probability of a win by Slick Joe to be 3/5. According to the gambler, what are
the odds in favor of Slick Joe winning? - Answer-Odds in favor=successes OVER failures
Probability= successes OVER outcomes
5-3=2
Answer is= 3/2
Another gambler assesses the odds against Slick Joe's winning to be 2 to 1. Find the gambler's
assessment of the probability that Slick Joe will win. - Answer-Odds against=failures OVER successes
Odds against= 2/1
2+1=3
P(win)=successes OVER outcomes =1/3
A small box contains twenty marbles. Eight of them are green, seven are red, and five are blue. What is
the probability that you will reach into the box and draw out
A. a blue marble?
B. a green or red marble?
C. If you are going to draw out three marbles, one at a time, and you are not going to replace the
marbles in the box once they are drawn, what is the probability that all three will be blue? - Answer-8
green
7 red
5 blue
total 20
A. P(blue)= 5/20=1/4
B. P(green or red)=8/20+7/20=15/20=3/4
C. P(all blue)=P(B&B&B)=5/20x4/19x3/18=60/6840=1/114
