To increase popularity a TV show announces prize money of 50000 daily and ask 4 questions, with only one caller for a question. The probability of the caller giving the correct answer is 0.4. Find the expected value of the number of correct answers.(Hint: Write your answers up to one decimal point)
Answers
Given : to increase popularity a tv show announces prize money of 50000 daily
Daily ask 4 questions with only one caller
The probability of the caller giving correct answer is 0.4
To Find : the expected value of the no of correct answers?
Solution:
n = 4
p = 0.4
q = 1 - p = 0.6
P(x) = ⁿCₓpˣqⁿ⁻ˣ
E(x) P(x) E(x) .P(x)
0 ⁴C₀(0.4)⁰(0.6)⁴ = 0.1296 0
1 ⁴C₁(0.4)¹(0.6)³ = 0.3456 0.3456
2 ⁴C₂(0.4)²(0.6)² = 0.3456 0.6912
3 ⁴C₃(0.4)³(0.6)¹ = 0.1536 0.4608
4 ⁴C₄(0.4)⁴(0.6)⁰ = 0.0256 0.1024
∑E(x) .P(x) 1.6
the expected value of the no of correct answers = 1.6
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