A binomial experiment has 6 trials in which p = 0.85. What is the probability of getting at least 4 successes? A) 0.9527

A binomial experiment has 6 trials in which p = 0.85. What is the probability of getting at least 4 successes?
A) 0.9527
B) 0.9178
C)0.4554

2 thoughts on “A binomial experiment has 6 trials in which p = 0.85. What is the probability of getting at least 4 successes? A) 0.9527<br /”

  1. Answer:
    0.9527
    Step-by-step explanation:
    Once again, if Brainly would stop deleting my answer for no reason, your answer is 0.9527. OKAY! …okay

    Reply
  2. The binomial probability for getting at least 4 successes is 0.955

    What is binomial probability?

    The probability of exactly x successes on n repeated trials in an experiment which has two possible outcomes is called binomial probability.

    Binomial probability formula

    [tex]P_{x} = nC_{x} p^{x} q^{n-x}[/tex]
    Where,  
    P is the binomial probability
    x is the number of times for a specific outcomes within n trials
    [tex]nC_{x}[/tex] is the number of combinations
    p is the probability of success in a single trial
    q is the probability of failure on a single trial
    n is the number of trials
    Let p denote the probability of getting success in a single trial and q denotes the probability of failure in a single trial.
    And let x be a random variable denoting the number of success.
    According to the given question.
    We have
    [tex]p = 0.85[/tex]
    ⇒[tex]q = 1- 0.85 = 0.15[/tex]
    Also,
    n = 6
    Therefore,
    The  binomial probability of getting at least 4 success
    [tex]=P(x\geq 4)[/tex]
    [tex]=P(x=4)+P(x=5)+P(x=6)[/tex]
    [tex]= 6C_{4} (0.85)^{4} (0.15)^{2} + 6C_{5} (0.85)^{5} (0.15)^{1}+ 6C_{6} (0.85)^{6} (0.15)^{0}[/tex]
    [tex]=\frac{6!}{4!21} (0.522)(0.0225)+\frac{6!}{5!1!} (0.443)(0.15)+\frac{6!}{6!0!} (0.4)[/tex]
    [tex]=15(0.011)+6(0.066)+1(0.4)[/tex]
    [tex]=0.165+0.396+0.4\\=0.955[/tex]
    Hence, the binomial probability for getting at least 4 successes is 0.955
    Thus, option A is correct.
    Find out more information about binomial probability here:
    #SPJ3

    Reply

Leave a Comment