A group of patients select from among 38 numbers, with 18 odd numbers (black) and 18 even
numbers (red), as well as 0 and 00 (which are green). If a doctor pays $7 that the outcome is an odd
number, the probability of losing the $7 is 20/38 and the probability of winning $14 (for a net gain of
only $7, given you already paid $7) is 18/38
If a doctor pays $7 that the outcome is an odd number, how would you figure out what is the doctors
expected value is?

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JeanaShupp JeanaShupp · Answer 1 · 2020-08-08T04:47:56+02:00

Answer: $2.95

Step-by-step explanation:

Given: Probability of losing the $7 = [tex]\dfrac{20}{38}[/tex]

Probability of winning $14 = [tex]\dfrac{18}{38}[/tex]

Then, the expected value = (- $7) x ( Probability of losing the $7) + $14 x(Probability of winning $14)

= [tex](-\$ 7)\times\dfrac{20}{38}+(\$14)\times\dfrac{18}{38}[/tex]

= [tex]-\dfrac{70}{19}+\dfrac{126}{19}[/tex]

= [tex]\dfrac{56}{19}\times\approx\$2.95[/tex]

∴ If a doctor pays $7 that the outcome is an odd number, the doctor's

expected value is $2.95.