Unit 8

Given the vectors , , and , express the vector as a column vector. Then, calculate its magnitude, giving your answer correct to 1 decimal place.

A vector has a magnitude of 13 and makes an angle of with the positive -axis. Prove that the vector could be , giving your reasoning using the definitions of vector magnitude and direction.

Sam throws a coin once. What is the probability that it lands on heads?

A bag contains 5 green balls and 3 yellow balls. Kate picks a ball at random, replaces it, and then picks again. What is the probability that both balls are green?

Mia flips two different coins. She draws a tree diagram to show the possible outcomes. Explain why a tree diagram is helpful for finding the probabilities of different results.

A number card is chosen at random from a box containing 6 cards numbered 1 to 6. The card is replaced and another card is chosen.

What do the branches in a probability tree diagram represent?

The probability that Amira will be chosen for the school play is 0.3. What is the probability that she is not chosen for the play?

The table shows the probability that a spinner will land on each colour.

a) Write down the value of .

A box contains 7 blue pens and 5 red pens. A pen is selected at random. It is replaced, and then another pen is selected at random. Find the probability of selecting a blue pen both times.