Question

An unfair coin has a probability of coming up heads of 0.65. The coin is flipped 50 times. What is the probability it will come up heads 25 or fewer times? (Give answer to at least 3 decimal places).

Answer 1

Answer: the probability it will come up heads 25 or fewer times is 0.019

Step-by-step explanation:

Given that;

n = 50

p = 0.65

so, q = 1 - p = 0.35

np = 50 × 0.65 = 32.5 ≥ 10

nq = 50 × 0.35 = 17.5 ≥ 10

so, we need to use Normal Approximation for the Binomial Distribution

μ = np = 50 × 0.65 = 32.5

σ = √(npq) = √( 50 × 0.65 × 0.35 ) = 3.3726

now, the probability that it will come up heads 25 or few times will be;

⇒ P( x≤25)

{using continuity correction}

⇒ P[ z < (25.5 - 32.5)/3.3726 ]

⇒ P[ z < -2.0755 ]

using z-table

= 0.01923 ≈ 0.019  { 3 decimal places}

Therefore the probability it will come up heads 25 or fewer times is 0.019