Question

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)​

Answer 1

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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