Venn Diagrams
Tree Diagrams
Probability Distributions
Calculating Probabilities
Pot Luck
100
Write the probability represented by the shaded region using set notation:
P(A'capB)
100
A bag contains blue and green beads. Two beads are chosen at random. What is the probability that the beads are different colours?
35/66
100
Name the type of probability distribution shown in the graph.
Discrete uniform distribution
100
The random variable X can take any integer value from 1 to 50. Given that X has a discrete uniform distribution, find P(13 < X < 42).
0.56
100
The Venn diagram shows the number of students who like either cricket (C), football (F) or swimming (S). Which two sports are mutually exclusive?
Cricket and Swimming
200
A patient going into a doctor's waiting room reads Hiya magazine with a probability of 0.6 and Dakor magazine with a probability of 0.4. The probability that the patient reads either one or both of the magazines is 0.7. Draw a Venn diagram to represent this data.
200
The probability that Charlie takes the bus to school is 0.4. If he doesn't take the bus, he walks. The probability that Charlie is late to school if he takes the bus is 0.2 The probability that he is late if he walks is 0.3. Draw a tree diagram to represent this information.
200
A bag contains two discs with the number 2 on them and two discs with the number 3 on them. A disc is drawn at random from the bag and the number noted. The disc is returned to the bag. A second disc is then drawn from the bag and the number noted. The discrete random variable X is defined as the sum of the two numbers. Write down the probability distribution of X.
200
P(A)=0.15 and P(A and B)=0.045. Given that events A and B are independent, find P(B).
0.3
200
W and X are two events such that P(W)=0.5, P(W and not X)=0.25 and P(neither W nor X)=0.3. State, with a reason, whether W and X are independent events.
P(W)xxP(X)=0.225. P(WcapX)=0.25.` So W and X are not independent.
300
The probability that a child in school has blue eyes is 0.27 and the probability that they have blonde hair is 0.35. The probability that the child will have blonde hair or blue eyes or both is 0.45. A child is chosen at random from the school. Find the probability that the child has blonde hair but not blue eyes.
0.18
300
A bag contains 13 tokens, 4 coloured blue, 3 coloured red and 6 coloured yellow. Three tokens are taken from the bag. Write down the probability that the third token is yellow, given that the first two are yellow.
4/11
300
`The random variable X has probability function `P(X=x)=(3x-1)/26` for `x =1,2,3,4.` Construct the probability distribution of X.
300
A patient going into a doctor's waiting room reads Hiya magazine with a probability of 0.6 and Dakor magazine with a probability of 0.4. The probability that the patient reads either one or both of the magazines is 0.7. Find the probability that the patient reads Hiya magazine only.
0.3
300
The histogram shows the distribution of masses, in kg, of 50 newborn babies. Find the probability that a baby chosen at random has a mass greater than 3kg.
44/50
400
The Venn diagram shows the probabilities of members of a sports club taking part in various activities. A represents the event that the member takes part in archery. B represents the event that the member takes part in badminton. C represents the event that the member takes part in croquet. Given that P(B)=0.45, find x and y.
x=0.15, y=0.15
400
In a factory, machines A, B and C produce electronic components. Machine A produces 16% of the components, machine B produces 50% of the components and machine B produces the rest. Some of the components are defective. Machine A produces 4%, machine B 3% and machine C 7% defective components. Find the probability that a randomly selected component is defective.
0.0452
400
The discrete random variable X has a probability function as shown. Find the value of beta.
P(X=x)={(0.1, if x=-2,-1),(beta, if x=0,1),(0.2, if x=2,):}
beta = 0.3
400
The members of a cycling club are married couples. For any married couple in the club, the probability that the husband is retired is 0.7 and the probability that the wife is retired is 0.4. Given that the wife is retired, the probability that the husband is retired is 0.8. Two married couples are chosen at random. Find the probability that only one of the two husbands and only one of the two wives is retired.
0.2016
400
The lengths, in cm, of 240 koalas are recorded in a table. One koala is chosen at random. Koalas under 72cm long are called juvenile. Estimate the probability that a koala chosen at random is juvenile. State one assumption you have made in making your estimate.
2/15 ` Assumption: distribution of koalas between 70 and 75 is uniform.`
500
The Venn diagram shows the probabilities of a group of children liking three types of sweet. Given that P(B)=2P(A) and that P(C')=0.83, find the values of p, q and r.
p=0.115, q=0.365, r=0.12
500
A group of students were surveyed by a principal and 2/3 were found to always hand in assignments on time. When questioned about their assignments 3/5 said they always start their assignments on the day they are issued and, of those who always start their assignments on the day they are issued, 11/20 hand them in on time. Find the probability that a randomly selected student does NOT start on the day the assignment is set, but DOES hand it in on time.
101/120
500
The random variable X has a probability function. Find P(X>1)
P(X=x)={(kx,x=1,3),(k(x-1),x=2,4):}
0.875
500
The independent random variables X and Y have probability distributions as shown. Find P(X>Y)
P(X=x)=1/8, x=1,2,3,4,5,6,7,8` and `P(Y=y)=1/y, y=2,3,6.
0.625
500
The Venn diagram shows the probabilities that a group of children like cake (A) or crisps (B). Determine whether the events A and B are independent.
Not independent