Answer: 24) d 25) d 26) d 27) a
<u>Step-by-step explanation:</u>
24)
a) a card can be red and a diamond --> Not mutually exclusive
b) a sum of 8 can include an even number (e.g. 2 + 6) --> Not mutually exclusive
c) a black card can be a Queen --> Not mutually exclusive
d) a 3 CANNOT be an even number --> Mutually exclusive!
25)
In order for event A and event B to be mutually exclusive, they cannot intersect --> P(A ∩ B) = 0
26)
P(B) = 0.34
P(A ∪ B) = 0.62
p(A ∩ B) = 0 <em>because they are mutually exclusive </em>
--> P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
0.62 = P(A) + 0.34 - 0
0.28 = P(A)
--> P(A)' = P(not A)
= 1 - P(A)
= 1 - 0.28
= 0.72
27)
hockey game = P(A) = 0.4
dance = P(B) = 0.5
hockey or dance = P(A ∪ B) = 0.8
--> hockey and dance = P(A ∩ B)
P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
0.8 = 0.4 + 0.5 - P(A ∩ B)
- 0.1 = -P(A ∩ B)
0.1 = P(A ∩ B)
