Question 1152662

Given a binomial distribution with n = 5 and  π=  .25. Determine the probabilities of the following events using the binomial formula. (Round your answers to 4 decimal places.)

a) x = 2
b) x = 3
<pre><b>a)</b> Using the BINOMIAL PROBABILITY formula, we get: {{{highlight_green(matrix(1,7, " "[n]C[x] * p^x * q^(n - x), "=====>", " "[5]C[2] * (.25)^2 * (1 - .25)^(5 - 2), "======>", 10 * (.25)^2 * .75^3, "=", highlight(.2637))))}}}  
<b>b)</b> Using the BINOMIAL PROBABILITY formula, we get: {{{highlight_green(matrix(1,7, " "[n]C[x] * p^x * q^(n - x), "=====>", " "[5]C[3] * (.25)^3 * (1 - .25)^(5 - 3), "======>", 10 * (.25)^3 * .75^2, "=", highlight(.0879))))}}}