Probability exercises:
Consider the experiment of selecting a card from an ordinary deck of 52 playing cards. Determine the
probability of each outcome.
An ordinary deck consists of 4 sets of 13 cards each. The sets are hearts, diamonds, spades and clubs.
Each set has three face cards (Jack, Queen & King).
Two sets are red (Hearts and diamonds), two are black (spades and clubs) in colour.
Determine the probability of each outcome:
1.A red card or a card showing a 5 is drawn.
2.A non-face card or a 7 is drawn.
3.A card drawn is neither a king nor a spade.
4.A card that is a black face card is drawn.
5. A card that is not a face card is drawn.
A box contains three red balls and two white balls. A ball is selected at random from the box, its color is
recorded, and the ball is replaced. A second ball is then selected at random and its color is recorded. The
outcome associated with this type of selection is an ordered pair (first drawn second draw). An example
outcome is (red,white).
6.List the sample space for this experiment.
7.Determine the probability that both balls are red.
8.Determine the probability that both balls are white.
9.Explain why the probabilities determined for (7) and (8) do not sum to 1.
10.Suppose we know that probability for event A = 0.65. What is the probability of event A not occurring
?
A family has three children, ages 5, 7, and 10. If we assume that the probability of giving birth to a boy is
the same as the probability of giving birth to a girl, determine the following probabilities.
11.P(three girls)
12.P(at least two boys)
13.P(the oldest is a girl)
14.P(two children are of the same gender)
15.P(there are an equal number of boys and girls)
Three different gaming machines were on exhibit at a local casino. A sign on each machine showed its
sample space (in dollars) and the probability of each guaranteed output in the sample space.
16.If you wanted to select the machine that produced the largest average (mean) output over a long
time period, which machine would you select? Explain.
17.Suppose that you and two friends are beginning to play the three machines. If you have first choice
on which machine you'll play, which of the three would you choose? Explain.
18.A fair die is rolled three consecutive times. What is the probability that the digit sum of the three rolls
is 15 or larger?
19.A fair die is rolled six times. Determine the probability that each of the six equally likely outcomes
appears exactly once in those six rolls.
A production line is equipped with two quality-control check points that tests all items on the line. At
check point #1, 10% of all items failed the test. At check point #2, 12% of all items failed the test. We
also know that 3% of all items failed both tests.
20.If an item failed at check point #1, what is the probability that it also failed at check point #2?
21.If an item failed at check point #2, what is the probability that it also failed at check point #1?
22.What is the probability that an item failed at check point #1 or at check point #2?
23.What is the probability that an item failed at neither of the check points?
George knows that a rare disease, D, within his family can be passed on to his children, and that the
probability is 0.10 that the inherited disease will be passed on to a child. We signify this at P(D) = 0.10.
24.Determine the probability that none of George's three children inherit the disease from George.