Lesson 68 Mutually exclusive and inclusive events probability

Lesson 68 Mutually exclusive and inclusive events

probability • Probability describes the possibility of an event happening. In some cases, the events cannot happen at the same time. For example: when someone tosses a fair coin, there are 2 possible outcomes: heads or tails. Both cannot occur at the same time. • 2 events that cannot both occur at the same time are mutually

Probability of mutually exclusive events • if A and B are mutually exclusive events, then • P(A or B) = P(A) + P(B) • Example: what is the probability of rolling a sum of 6 or a sum of 11 on 2 different dice. • Mutually exclusive so P(6) + P(11) = • 5/36 + 2/26 = 7/36

practice • What is the probability of rolling a sum of 5 or a sum of 12 on 2 different dice?

Inclusive events • Sometimes it is possible for 2 events to happen at the same time. 2 events are mutually inclusive events, or joint events, if they can occur at the same time • the probability of inclusive events is the same as finding the probability of exclusive events, and then subtracting the events they have in common. • Probability of inclusive events • If A and B are mutually inclusive events,

Finding probability of inclusive events • What is the probability of rolling at least one odd number or a sum of 8 using 2 dice? • First decide if they are inclusive: • Rolling 1 odd number: (1, 1)(1, 2)(1, 3)(1, 4)(1, 5)(1, 6)(3, 1)(3, 2)(3, 3)(3, 4)(3, 5) • (3, 6)(5, 1)(5, 2)(5, 3)(5, 4)(5, 5)(5, 6)(2, 1)(2, 3)(2, 5)(4, 1) (4, 3)(4, 5) • (6, 1)(6, 3)(6, 5) • Rolling a sum of 8: • (2, 6)(3, 5)(4, 4)(5, 3)(6, 2) • P(A or B) = P(odd) + P(8) -P(odd or 8)

practice • What is the probability of rolling at least 1 even number or a sum of 10 using 2 dice?