S1 Chapter 5 Probability – – Exercise 1 Probabilities by Enumerating Outcomes – (Note: some earlier parts of questions have been omitted because they relate to a later chapter) The score when a spinner is spun has the following probability distribution. Slide Example: S 0 1 2 4 5 s P(s) 0.2 0.2 0.1 0.3 0.2 The spinner is spun twice. The from the first spin is and the score from the second spin is S1 S2. The random variables and are independent and the random variable = × S1 S2 X S1 S2. (f) Show that P({S1 = 1} < 5) = 0.16. (2) X ∩ (g) Find P(X < 5). (3) Jim rolls an unfair die with the following probability distribution: 6 1 2 3 4 5 d 0.1 P(d) 0.4 0.3 0.1 0.05 0.05 Calculate the probability that, after throwing the die twice: a) He rolls a 2 followed by a number greater than 3. b) He rolls a total of at most 3. c) He rolls a total of at least 10. d) He rolls a product of 6. When plays a game, the number of points he receives is given by the event 2. [Jan 2009 Q3] X with the following probability distribution. 0 1 2 3 x P( 0.4 0.3 0.2 0.1 x) Rohit can win a prize if the total number of points he has scored after 5 games is at least 10. After 3 games he has a total of 6 points. You may assume that games are independent. (e) Find the probability that Rohit wins the prize. (6) 3. [Jan 2013 Q6f] A fair blue die has faces numbered 1, 1, 3, 3, 5 and 5. The event represents the B score when the blue die is rolled. A second die is red and the event represents the score when the red die is rolled. R The probability distribution of is R 2 4 6 r P(r)
S1 – Chapter 5 – Probability Exercise 1 – Probabilities by Enumerating Outcomes (Note: some earlier parts of questions have been omitted because they relate to a later chapter) Slide Example: The score S when a spinner is spun has the following probability distribution. s 0 1 2 4 5 P(s) 0.2 0.2 0.1 0.3 0.2 The spinner is spun twice. The from the first spin is S1 and the score from the second spin is S2. The random variables S1 and S2 are independent and the random variable X = S1 × S2. (f) Show that P({S1 = 1} ∩ X < 5) = 0.16. (2) (g) Find P(X < 5). (3) Jim rolls an unfair die with the following probability distribution: d 1 2 3 4 5 6 P(d) 0.4 0.3 0.1 0.05 0.05 0.1 Calculate the probability that, after throwing the die twice: a) He rolls a 2 followed by a number greater than 3. b) He rolls a total of at most 3. c) He rolls a total of at least 10. d) He rolls a product of 6. 2. [Jan 2009 Q3] When plays a game, the number of points he receives is given by the event X with the following probability distribution. x 0 1 2 3 P( x) 0.4 0.3 0.2 0.1 Rohit can win a prize if the total number of points he has scored after 5 games is at least 10. After 3 games he has a total of 6 points. You may assume that games are independent. (e) Find the probability that Rohit wins the prize. (6) 3. [Jan 2013 Q6f] A fair blue die has faces numbered 1, 1, 3, 3, 5 and 5. The event B represents the score when the blue die is rolled. A second die is red and the event R represents the score when the red die is rolled. The probability distribution of R is r 2 4 6 P(r)
S1-Chp5-Probability-Exercises.docx