Math Studies Probability Review

The tree diagram below represents the probability of being an IB student at Creek and going to college.

Find:

P( the student is in IB and goes to college)

P(the student is not in IB and doesn’t go to college)

P(the student does not go to college)

The tree diagram below represents the probability of living in a dorm at college.

Find:

P(IB or living in a dorm, but not both)P(student doesn’t live in a dorm)

P(student does live in a dorm)P(IB given that they live in a dorm)

P(not IB given that they don’t live in a dorm)

P(not IB and went to college and lived in a dorm)

From experience, it is known that a packet of seeds contains 80% viable seeds. If viable seeds are planted then 90% are expected to grow into plants; and if non-viable seeds are planted then 15% are expected to grow into plants.

a)i) Draw a tree diagram to represent this information.

ii) A farmer sows the seeds from packets containing 1000 seeds. How many plants does he expect to grow?

b) i) Find the probability that a randomly selected seed from a packet of seeds will grow into a plant.

ii) A farmer grows a plant from a seed randomly selected from a packet. Find the probability that the plant is grown from a viable seed.

c) A packet contains 20 seeds. A farmer randomly selects 3 seeds from a packet.

i) What is the probability that all 3 seeds are non-viable?

ii) What is the probability that at least on seed is non-viable?

iii) What is the probability that exactly on seed is viable?

A fair six-sided die had the numbers 1,2,3,4,5,6 written on its faces. A fair four-sided die has the numbers 1,2,3,4 written on its faces. The two dice are rolled at the same time.

a) Make a diagram showing the possible outcomes.

b) Find the probability that the two dice show the same number.

c) Find the probability that the difference of the two numbers shown on the dice is 1.

d) Find the probability that the number shown on the four-sided die is greater than the number shown on the six-sided die, given that the difference between the two numbers

is 1.

For events A and B, the probabilities are P(A) = 4/15 and P(B) = 6/15.

a) If events A and B are mutually exclusive, write down the value of P(AB).

b) If the events A and B are independent, write down the value of P(AB).

c) If P (AB) = 7/15, find the value of P(AB).

Functional Robotics Corporation buys electric controllers from a Japanese supplier. The company’s treasurer feels that there is a probability of 0.4 that the dollar will fall in value against the yen in the next month. The treasurer also believes that if the dollar falls, there is probability 0.8 that the supplier will demand renegotiation of the contract. He also feels that if the dollar does not fall, there is a probability of 0.2 that the supplier will demand a renegotiation.

a) Draw a tree diagram representing the above probabilities.

b) What is the probability that the supplier will demand renegotiation?