Find the probability

Question

Spin the spinner and record the number that comes up (assume the spinner cannot stop on a dividing line).

A = odd number

B = number greater than 2

 

The Numbers in Spinner and their degrees:

1 : 140 Degrees

2: 50 Degrees

3: 110 Degrees

4: 40 Degrees

5: 20 Degrees

 

Questions:

a. Find P(A | B)

b. Are A and B independent?

c. Find P(A ∪ B)

Answer 1

Hi Jean,

 

a) P (A | B)

= P (A and B) / P (B)

= P (3 or 5) / P (3, 4, or 5)

= 130 / 170

 

b) P(A)

= P (1, 3, or 5)

= 270 / 360

Since P (A) ≠ P (A | B), A and B aren't independent

 

c) P (A ∪ B)

= 1 - P (A^c ∩ B^c)

= 1 - P (2)

= 1 - 50 / 360

= 310 / 360