2.5 A Recursion
107 11. An experimental rocket is launched 5 times. The probability of a successful launch
is 0.9. Let X denote the number of successful launches. A study has shown that the net cost of the experiment, in thousands of dollars, is 2 − 3X
2
. Find the expected net cost of the experiment.
12. Twenty percent of the IC chips made in a plant are defective. Assume that a
binomial model is appropriate.
a. Find the probability that, at most, 13 defective chips occur in a sample of 100. b. Find the probability that 2 samples, each of size 100, will have a total of exactly
26 defective chips.
13. A coin, loaded to come up heads with probability
2 3
, is tossed 5 times. If the number of heads is odd, the player is paid 5. If the number of heads is 2 or 4 the
player wins nothing; if no heads occur, the player tosses the coin 5 more times and wins, in dollars, the number of heads thrown. If the game costs 3 to play, find the
probability distribution of N , the player’s net winnings.
14. a. Show that the probability of being dealt a full house 3 cards of one value and
2 of another value in poker is about 0.0014.
b. Find the probability that in 1000 hands of poker you will be dealt at least 2 full
houses.
15. An airline knows that 10 of the people holding reservations on a given flight will
not appear. The plane holds 90 people.
a. If 95 reservations have been sold, find the probability that the airline will be
able to accommodate everyone appearing for the flight.
b. How many reservations should be sold so that the airline can accommodate
everyone who appears for the flight 99 of the time?
16. The probability that an individual seed of a certain type will germinate is 0.9.
A nurseryman sells flats of this type of plant and wants to “guarantee” with probability 0.99 that at least 100 plants in the flat will germinate. How many
plants should he put in each flat?
17. A coin with P. H =
1 2
is flipped 4 times and then a coin with P. H =
2 3
is tossed twice. What is the probability that a total of 5 heads occurs?
18. a. Each of 2 persons tosses 3 fair coins. What is the probability each gets the
same number of heads?
b. In part a, what is the probability that X
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