Assume that when adults with smartphones are randomly selected, 51 % use them in meetings or classes. If 9 adult smartphone users are randomly selected, find the probability that at least 2 of them use their smartphones in meetings or classes.
Let X be number of adults who use their smartphones in meetings or classes.
Here, X ~ Binomial ( n = 9, p = 0.51)
probability mass function of X is,
P(X = x) = nCx px (1-p)n-x
We want to find, P(X >= 2)
P(X>=2)
= 1 - P(X < 2)
= 1 - [ P(X = 0) + P(X = 1) ]
= 1 - [ 9C0 * (0.51)0 * (0.49)9 + 9C1 * (0.51)1 * (0.49)8 ]
= 1 - [ 1 * 1 * (0.49)9 + 9 * (0.51) * (0.49)8 ]
= 1 - [ 0.0016 + 0.0153 ]
= 1 - 0.0169
= 0.9831
=> P(X >= 2) = 0.9831
Therefore, the probability that at least 2 of them use their smartphones in meetings or classes is 0.9831
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