Probability concepts; complementary events; expected occurrences practice questions.

The probability that it rains on a given day is P(R) = 0.35. Calculate the probability that it does not rain on that day.

• 0.35
• 0.65
• 0.70
• 1.35

Answer: 0.65

For complementary events, P(not R) = 1 - P(R) = 1 - 0.35 = 0.65.

A spinner lands on red with probability 0.2. If it is spun 150 times, calculate the expected number of times it lands on red.

• 30
• 75
• 20
• 120

Answer: 30

Expected occurrences = n × p = 150 × 0.2 = 30.

A bag contains 3 red, 5 blue and 2 green marbles. One marble is drawn at random. Determine the probability that it is NOT blue.

• 1/2
• 1/5
• 7/10
• 3/10

Answer: 1/2

P(blue) = 5/10, so P(not blue) = 1 - 5/10 = 5/10 = 1/2.

Two events A and B are mutually exclusive, with P(A) = 0.3 and P(B) = 0.45. Calculate P(A ∪ B).

• 0.135
• 0.75
• 0.15
• 0.60

Answer: 0.75

For mutually exclusive events P(A ∪ B) = P(A) + P(B) = 0.3 + 0.45 = 0.75, since P(A ∩ B) = 0.

In a class of 30 students, the probability that a randomly chosen student wears glasses is 0.4. Determine the expected number of students who do NOT wear glasses.

• 12
• 18
• 0.6
• 24

Answer: 18

P(no glasses) = 1 - 0.4 = 0.6; expected number = 30 × 0.6 = 18.

Events A and B satisfy P(A) = 0.5, P(B) = 0.4 and P(A ∩ B) = 0.2. Calculate P(A ∪ B).

• 0.9
• 1.1
• 0.7
• 0.2

Answer: 0.7

P(A ∪ B) = P(A) + P(B) - P(A ∩ B) = 0.5 + 0.4 - 0.2 = 0.7.