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Step-by-step explanation:
How do you calculate number of successes?
Example:
Define Success first. Success must be for a single trial. Success = "Rolling a 6 on a single die"
Define the probability of success (p): p = 1/6.
Find the probability of failure: q = 5/6.
Define the number of trials: n = 6.
Define the number of successes out of those trials: x = 2.
Binomial probability distribution for the given set of data is
[tex]\ 100C_{x[/tex][tex]( 0.20)^{x} (0.80)^{100-x}[/tex].
"Binomial probability distribution is the representation of a probability with only two outcomes success and failure under given number of trials."
Formula used
Binomial probability distribution is given by
[tex]\\n{C}_{x}p^{x}q^{n-x}[/tex]
n= number of experiments
x = 0, 1, 2, 3,.......
p = probability of success
q = probability of failure
According to the question,
Number of trials 'n' = 100
Probability of success 'p' = (20 / 100)
= 0.20
Probability of failure 'q' = 1 - p
= 1 - (20/100)
= (80 / 100)
Substitute the value in the formula we get
Required probability = [tex]\ 100C_{x[/tex][tex]( 0.20)^{x} (0.80)^{100-x}[/tex]
Example:
Tossing a coin 6 times getting exactly two heads.
Number of trials 'n' = 6
Number of heads 'x' =2
Only two possible outcomes head or tail
Probability of getting head 'p' = 1 / 2
Probability of not getting head 'q' = 1 /2
Required probability = [tex]\ 6C_{2[/tex] (1/2)²(1/2) ⁶⁻²
=[tex]\ 6C_{2[/tex] (1/2)⁶
Hence, binomial probability distribution for the given set of data is
[tex]\ 100C_{x[/tex][tex]( 0.20)^{x} (0.80)^{100-x}[/tex]
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