Probability
1. The
probability that a man will be alive in 20 years is 3/4
and the probability that his wife will also be alive in 20 years is 4/5.
Find the probability that at least one of them will be alive in 20years.
2. A
paper bag A contains 3 red ball gums and 5 yellow ones. Another paper B
contains 4 red ball gums and 6 yellow ones. A paper bag is chosen at random and
a ball gum is picked from it, Find the probability that the ball gum is yellow.
3. Three
boys, Otieno, Kamau and Mutiso compete a word puzzle. The probabilities of
getting it correct for each of them is as follows. Otieno 3/5, Kamau 2/3 and Mutiso 3/4. Find the probability that
a.
None
of them gets it correct
b.
At
least one gets it correct.
c.
Exactly
one gets it correct
d.
Exactly
two gets it correct given that Kamau has it correct.
4. In
a unique knockout beach volley ball that involves three teams A, B and C, teams
A and B must start playing. Only the team that wins the game one proceeds to
play team C. The chances that B wins in the first game are 3/5.
If B does not win, the chance that C eventually wins in the next match is 5/7.
If B wins the first game, the chance that it again wins the second game against
C is 4/7.
a.
Draw
a tree diagram to represent this information.
b.
Find
the probability that
i.
Team
A emerges the eventual winner
ii.
Team
B does not eventually win.
iii.
Team
C emerges the eventual winner.
iv.
Team
C does not eventually win.
5. The probability that James will be
selected for the school’s basketball team is 2/5 and the
probability that Ken will not be selected for the same team is 2/7.
Fid the probability that
a. Both
will be selected.
b. At
least one will be selected.
6. The
probability that a student passes mathematics paper one is 3/5.
The probability that he passes paper two depends on whether or not he passes
paper one, and is 1/2 if he passes paper one and 3/10
if he fails. Find the probability that he passes in only one paper.
7. If
the probability that it is raining when you go to school is 1/3
and that it is not raining when you come out of school is 1/6,
what is the probability that it is raining
a.
On
both occasions
b.
On
one occasion and not in the other.
8. A
room is lit by two light bulbs, A and B. The probability of light A failing is 1/10
and that of light B failing is 1/12. Find the probability
that
a.
Both
are working
b.
There’s
some light in the room.
9. There
are two packets of sweets labelled A and B. Packet A contains 4 yellow, 3 red
and 5 green sweets while packet B contains 3 yellow, 7 red and 5 green sweets.
A child selects a packet at random and picks a sweet from it. Determine the
probability that he picks a yellow sweet.
10. The
probability that a day is wet is 3/5. The probability
that I wear gumboots on a wet day is 4/9 and that I wear
gumboots on a dry day is 3/8. Find the probability that
a.
I
will wear gumboots
b.
It
will be wet and I wear gumboots.
c.
It
will not be wet and I will not wear gumboots.
11. Tom has 5 white balls and 4 blue balls in
a bag. He draws out one ball at a time without replacing if in the bag. Use a
tree diagram to find the probability that he will get two balls of different
colours in the first two draws.
12. A student travels to school by either bus of
matatu. The probability that he travels by bus is 2/3. If
he travels by bus, the probability that he will be late is 1/4
while if he travels by matatu, the probability that he will not be late is 3/5.
Find the probability that he
a.
Travels
by matatu and gets late
b.
Does
not get late.
13.
The
probability of Martin passing in mathematics is 7/10. If
he passes, the probability of joining a computer college is 4/9
and when he fails is 1/5. Using a tree diagram, find the
probability that he passes and fails to join the computer college.
14.
Every
afternoon during preps time, Peter either reads a novel of solves Mathematics
questions. The probability that he reads a novel is 4/5.
If he reads a novel, the probability that he falls asleep is 3/4
otherwise it is 1/4. Sometimes the teacher on duty enters
Peter’s classroom. When Peter is asked whether he had been asleep, the
probability of him admitting is 1/5 and 3/5
that he will claim to have been asleep when he had been awake. Find the
probability that
a.
He
sleeps and admits it
b.
He
sleeps and does not admit it
c.
He
does not sleep but claims to have been asleep.
d.
He
does not sleep and says that he was not asleep.
15. In a science class, 2/3
of the class are boys and the rest are girls. 4/5 of the
boys and 9/10 of the girls are right-handed. The
probability that a right-handed student will break a test-tube in any session
is 1/10 and that for a left-handed student is 3/10.
a.
Draw
a tree diagram to represent this information.
b.
Determine
the probability that
i.
A
student chosen at random from the class is left-handed.
ii.
A
test-tube is broken in any session.
