1.1. Independent Events http://www.ck12.org
P(A∪B) =P(A)+P(B)−P(A∩B)
P(A∩B) =0 for mutually exclusive eventsExample 5:Two cards are drawn from a deck of cards. The first card is replaced before choosing the second card.
A: 1stcard is a club
B: 1stcard is a 7
C: 2ndcard is a heart
Find the following probabilities:
(a)P(AorB)
(b)P(BorA)
(c)P(AandC)
Solution:
(a)
P(A or B) =13
52
+
4
52
−
1
52
P(A or B) =16
52
P(A or B) =4
13
(b)
P(B or A) =4
52
+
13
52
−
1
52
P(B or A) =16
52
P(B or A) =4
13
(c)
P(A and C) =13
52
×
13
52
P(A and C) =169
2704
P(A and C) =1
16
Let’s go back to our original problem now and see if we can solve it.
Bias and Probability
B. Eric Hawkins is taking science, math, and English, this semester. There are 30 people in each of his classes. 25
passed the science mid-semester test, 24 passed the mid semester math test, and 28 passed the mid-semester English
test. He found out that 4 students passed both math and science tests. Eric found out he passed all three tests.
(c) Draw a VENN DIAGRAM to represent the students who passed and failed each test.
(d) If a student’s chance of passing math is 70%, and passing science is 60%, and passing both is 40%, what is the
probability that a student, chosen at random, will pass math or science.
(a)