Respuesta :
The probability of getting the fewer than four twos is 0.5665.
Explain the Binomial probability distribution?
- The probability of precisely x successes after n repeated trials is known as a binomial probability, and X only has two possible outcomes.
P(X = x) = C(n,x). p ˣ .(1 - p)ⁿ⁻ˣ
- Where C(n,x) is the number of distinct combinations of x items drawn from a group of n elements, as determined by the formula below.
C(n,x) = n!/x!(n-x)!
For the given question-
p is the likelihood that X will occur.
20 times of a die are rolled;
This indicates that; n = 20.
Six sides, one of which is two:
This indicates that; p = 1/6 = 0.1667.
Probability of having three or fewer twos:
Such is:
P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)
So,
P(X < 4) = C(n,x). p ˣ .(1 - p)ⁿ⁻ˣ
P(X = 0) = C(20,0). 0.1667⁰ .(0.8333)²⁰
P(X = 0) = 0.0261
P(X = 1) = C(20,1). 0.1667¹ .(0.8333)¹⁹
P(X = 1) = 0.1043
P(X = 2) = C(20,2). 0.1667 ² .(0.8333)¹⁸
P(X = 2) = 0.1982
P(X = 3) = C(20,3). 0.1667³ .(0.8333)¹⁷
P(X = 3) = 0.2379
P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)
P(X < 4) = 0.0261 + 0.1043 + 0.1982 + 0.2379
P(X < 4) = 0.5665
Thus, the probability of getting the fewer than four twos is 0.5665.
To know more about the Binomial probability distribution, here
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