Question

In the binomial probability distribution, let the number of trials be n = 4, and let the probability of success be p = 0.3418. Use a calculator to compute the following.
(a) The probability of three successes. (Round your answer to three decimal places.)
(b) The probability of four successes. (Round your answer to three decimal places.)
(c) The probability of three or four successes. (Round your answer to three decimal places.)

Answer 1

Answer:  (a) 0.105   (b) 0.014  (c) 0.119

Step-by-step explanation:

Binomial probability distribution formula :

$P(X=x)= \ ^nC_x p^x(1-p)^{n-x}$ , where x= number of successes, p= probability of success in each trial, n= number of trials.

Given: n= 4 , p= 0.3418

(a)

$P(X=3)=\ ^4C_3(0.3418)^3(1-0.3418)^1\\\\=(4)(0.026282946626)\\\\\approx0.105$

(b)

$P(X=4)=\ ^4C_4(0.3418)^4(1-0.3418)^0\\\\=(1)(0.013648604006)\\\\\approx0.014$

(c)

$P(X= 3\ o\r X=4)= P(X=3) +P(X=4)\\\\=0.105+0.014\\\\=0.119$