Probability concepts; complementary events; expected occurrences practice questions.

A bag contains 5 red, 3 blue and 4 green counters. One counter is taken at random. Determine the probability that it is not green.

• 1/3
• 5/12
• 2/3
• 3/4

Answer: 2/3

P(green) = 4/12 = 1/3, so by the complement rule P(not green) = 1 − 1/3 = 2/3.

The probability that a train arrives late is 0.35. State the probability that the train does not arrive late.

• 0.65
• 0.35
• 0.45
• 1.35

Answer: 0.65

Complementary events satisfy P(A') = 1 − P(A) = 1 − 0.35 = 0.65.

A spinner has 8 equal sectors numbered 1 to 8. It is spun 200 times. Calculate the expected number of spins that land on a multiple of 3.

• 25
• 75
• 66
• 50

Answer: 50

Multiples of 3 on the spinner are 3 and 6, so p = 2/8 = 1/4; expected occurrences = np = 200 × 1/4 = 50.

Two fair coins are tossed together. Determine the probability of obtaining at least one head.

• 1/4
• 1/2
• 3/4
• 2/3

Answer: 3/4

Use the complement: P(at least one head) = 1 − P(no heads) = 1 − 1/4 = 3/4.

A biased die is rolled 500 times and shows a six on 80 of the rolls. State the best estimate of the probability of rolling a six with this die.

• 1/6
• 0.2
• 0.16
• 0.8

Answer: 0.16

The relative frequency 80/500 = 0.16 is the best experimental estimate; 1/6 would only apply to a fair die.

Two fair six-sided dice are rolled and the scores are added. Determine the probability that the total is 7.

• 1/6
• 1/12
• 7/36
• 1/7

Answer: 1/6

The sample space has 36 equally likely outcomes and 6 of them sum to 7, so the probability is 6/36 = 1/6.