Question

There is a group of kindergarten children observed who have two different shirt colors, red and blue. Red = 1 and Blue = 0. The sample size of 8 can be formed as 1 1 0 0 0 0 1 0. What is the probability that 6 or more children will come in with a red shirt? Please show all calculations and use of formulas to find the percentage.

Answer 1

This can be constructed as a Binomial probability as

(1) There are 2 outcomes Blue or Red

(2) The probability is the same every trial

(3) They are independent of each other

(4) There are a fixed number of trials

___________________

Please note

Binomial Probability = ⁿC_x * (p)^x * (q)^n-x, where n = number of trials and x is the number of successes.

Here n = 8, p = 1/2, q = 1 – p = 1/2.

P(At Least 6) = P(6) + P(7) + P(8)

P(X = 6) = ⁸C₆ * (0.5)⁶ * (q)^8-6 = 0.1094

P(X = 7) = ⁸C₇ * (0.5)⁷ * (q)^8-7 = 0.0313

P(X = 8) = ⁸C₈ * (0.5)⁸ * (q)^8-8 = 0.0039

P(6 or more) = 0.1094 + 0.0313 + 0.0039 = 0.1446

______________________________