10 E (part 1)
1 If P(A)=0.2,P(B)=0.4, and P(AnB)=0.05, find P(AUB).
0.55
A and B are mutually exclusive events.
If P(B)=0.45 and P(AUB)=0.8, find P(A).
0.35
2 A coin is tossed 3 times. Determine the probability of getting the following sequences of results:
a head, head, head
b) tail, head, tail
1/8, 1/8
5 Two marksmen fire at a target simultaneously. Jiri hits the target 70% of the time and Benita hits it
80% of the time. Determine the probability that:
they both miss the target
0.06
2 If P(A)=0.4,P(AUB)=0.9, and P(AnB)=0.1, find P(B).
0.6
6 Tickets numbered 1 to 15 are placed in a hat, and one ticket is chosen at random. Let A be the
event that the number drawn is greater than 11, and B be the event that the number drawn is less
than 8.
a Are A and B mutually exclusive?
Yes
3 A school has two photocopiers. On any given day, machine A has an 8% chance of malfunctioning
and machine B has a 12% chance of malfunctioning. Determine the probability that on any given
day, both machines will:
malfunction
0.0096
An archer hits the bullseye on average 2 out of every 5 shots. If
3 arrows are fired at the target, determine the probability that the
bullseve is hit: every time
8/125
3 If P(X)=0.6, P(Y)=0.5, and P(XUY)=0.9, find P(XnY).
0.2
6 Tickets numbered 1 to 15 are placed in a hat, and one ticket is chosen at random. Let A be the
event that the number drawn is greater than 11, and B be the event that the number drawn is less
than 8.
Find P(A), P(B), P(AUB).
4/15, 7/15, 11/15
3 A school has two photocopiers. On any given day, machine A has an 8% chance of malfunctioning
and machine B has a 12% chance of malfunctioning. Determine the probability that on any given
day, both machines will:
Work
0.8096
8 Two baskets each contain 5 red apples and 2 green apples. Celia chooses an apple at random from
each basket.
Draw a tree diagram to illustrate the possible outcomes.
Show answer
4 Suppose P(A)=0.25, P(B)=0.45, and P(AUB)=0.7. a) Find P(AnB).
0
7 A class consists of 25 students.
11 students are fifteen years old (F).
12 students are sixteen years old (S).
8 students own a dog (D).
7 students own a cat (C).
4 students do not own any pets (N).
A student is chosen at random. If possible, find:
a P(F)
11/25
4 A couple has 4 children, none of whom were adopted. Assuming boys and girls are born with equal
likelihood, find the probability that the children:
were born in the order boy, girl, boy, girl
were not born in the order boy, girl, boy, girl.
1/16, 5/16
An archer hits the bullseye on average 2 out of every 5 shots. If
3 arrows are fired at the target, determine the probability that the
bullseve is hit: the first two times, but not on the third shot
12/125
4 Suppose P(A)=0.25, P(B)=0.45, and P(AUB)=0.7. What can you say about A and B?
A and B are mutually exclusive
7 A class consists of 25 students.
11 students are fifteen years old (F).
12 students are sixteen years old (S).
8 students own a dog (D).
7 students own a cat (C).
4 students do not own any pets (N).
A student is chosen at random. If possible, find: P(FUD)
Not Possible
5 Two marksmen fire at a target simultaneously. Jiri hits the target 70% of the time and Benita hits it
80% of the time. Determine the probability that:
they both hit the target
0.56
For a particular household, there is a 90% chance that at the end of the week the rubbish bin is full,
and a 50% chance that the recycling bin is full, independently of one another.
a Draw a tree diagram to illustrate this situation.
Show answer