The probability that fewer than 4 of then use their smart phones in meetings or classes is 0.00030243747.
Step-by-step explanation:
Fewer than 4 means ,less than 4 which is any number less than 4 and not including 4. This is 3, 2,1 and 0. So you find the probability that exactly 3 of then use their smart phone, exactly 2 of them use their smart phones, exactly 1 of them use his/her smart phone and none of them.
Given that 52% use smartphones in meetings and classes =0.52
Thus the remaining 48% do not use smartphones in meetings and classes=0.48
For C(14,3) you will have "14 chose 3", number of ways of choosing 3 out of 14'
=(0.52)³ *(0.48)⁹=0.00019018714
For C(14,2) you will have "14 chose 2", number of ways of choosing 2 out of 14
=(0.52)²*(0.48)¹²=0.00004044841
For C(14,1) you will have "14 chose 1", number of ways of choosing 1 out of 14
=(0.52)¹*(0.48)¹³=0.000037337
For C(14,0) you will have "14 chose 0", number of ways of choosing 0 out of 14
=(0.52)⁰*(0.48)¹⁴=1*0.00003446492=0.00003446492
The probability that fewer than 4 of them use their smartphones in meetings or classes will be
0.00019018714 +0.00004044841+0.000037337+ 0.00003446492=0.00030243747
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Keywords : Probability, random variable, binomial distribution
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The probability that fewer than 4 adults use their smartphones in meetings or classes is 0.02019
Using the binomial probability relation :
P(x = x) = nCx * p^x * q^(n-x)
Where :
To define the probability that fewer than 4 use the smartphone in meetings or classes :
P(X < 4) = P(X = 3) + P(x = 2) + P(x = 1) + P(X = 0)
Using a binomial probability calculator :
P(X = 3) = 0.01595
P(x = 2) = 0.00368
P(x = 1) = 0.00052
P(X = 0) = 0.00003
Hence,
P(X < 4) = 0.01595 + 0.00368 + 0.00052 + 0.00003
P(X < 4) = 0.02019
Therefore, the probability of fewer than 4 using their smartphones in meeting or classes is 0.02019.
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