The first card drawn is a diamond OR a club?
Practice Probability Problems
1. A standard deck of cards is shuffled and three cards are drawn in a row and no cards are
returned to the deck. What is the probability that:
a. The first card drawn is a diamond OR a club?
b. The second card is the ace of hearts? (given that the first was a spade)
c. The third card is the 10 of diamonds?
d. All three were hearts?
2. The mean number of landings at HSV airport is said to be 5
per hour and follow a Poisson distribution. What is the
likelihood that on any given day, 8 planes will land between
10 and 11 AM?
3. A multiple choice exam was given with 25 questions, each
having only one correct answer out of 5 given alternatives.
Assuming a student made random guesses for the answers, what is the probability that:
a. Exactly 20 questions were answered correctly?
b. 15 or fewer were answered right?
c. More than 10 were answered correctly?
d. Six or more are answered WRONG?
4. Suppose your local state game commission has decided to limit the yearly ‘take’ of deer
to 5 per hunter based on studies done over the last decade. If the probability of killing a
deer on any given hunt is .06 (p), what is the probability that:
a. you could take your limit on the first hunt?
b. Zero deer are killed on the first hunt of the season?
c. Two or more deer are taken during the season?
d. fewer than five are bagged?
5. Your daughter has just decided to run for the
senior class president. Out of 200 students, the
probability that a student will vote for a female
president has been estimated to be only 3
percent. Assuming that all students vote, what
is the probability that she will receive
a. zero votes?
b. 10% or more of the votes?
c. less than 5% of the votes?
d. She receives exactly 10 votes?
Note: if n=> 100 AND p<0.05, use Poisson Distribution, otherwise use Binomial Distribution.
2013.01.31 JWMcCainPROBABILITY PRACTICE PROBLEMS – Solutions (Please work these out FIRST before looking @ these answers.)
#1A P(♦ OR ♣) = P(♦) + P(♣) = 13/52 + 13/52 = 26/52 = 0.5
#1B P(A♥/ ♠) = 1/51 = 0.0196
#1C P(10♦/A♥/♠) = 1/50 = 0.02
#1D P(♥/♥/♥) = P(♥) X P(♥) X P(♥) = 11/50 X 12/51 X 13/52 = 0.0129
#2 0.0653 = POISSON(8,5,FALSE) TRUE=CUMULATIVE; FALSE=NONCUMULATIVE
P( )
#3A 0.0000 = BINOMDIST(20,25,0.2,FALSE) X = 20 P = 1/5 = 0.2 :RIGHT ANSWER
#3B 1.0000 = BINOMDIST(15,25,0.2,TRUE) X ≤ 15
#3C 0.0056 = 1 – (BINOMDIST(10,25,0.2,TRUE)) X > 10
#3D 1.0000 = 1 – BINOMDIST(5,25,0.8,TRUE) X ≥ 6 Q = 1 – P = 1 – 0.2 = 0.8 : WRONG ANSWER
#4A 0.0000 = BINOMDIST(5,5,0.06,FALSE) X = 5
#4B 0.7339 = BINOMDIST(0,5,0.06,FALSE) X = 0
#4C 0.0319 = 1 – (BINOMDIST(1,5,0.06,TRUE)) X ≥ 2
#4D 1.0000 = BINOMDIST(5,5,0.06,TRUE) X ≤ 4
#5A 0.0025 = POISSON(0,6,FALSE) X = 0 µ = NP = 200 X .03 = 6.0
#5B 0.0000 = 1 – POISSON(19,6,TRUE) X ≥ 20
#5C 0.9161 = POISSON(9,6,TRUE) X < 10
#5D 0.0413 = POISSON(10,6,FALSE) X = 1
