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It is reported that 77% of workers aged 16 and over drive to work alone. Choose 8 workers at random. If X represents the random variable of driving to work alone, the following table depicts the probabilities for this case.

Find the following probabilities as percentages to 1 d.p.
a) Probability that none drives to work alone
b)Probability that exactly 5 drive to work alone
c)Probability that at most 4 drive to work alone.

Apr 15, 2020

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Probability of driving to work alone        =  0.77

Probability of not driving to work alone  =  0.23

Total number of workers                         =  8

Probability that none drive to work alone:        8C0·(0.77)0·(0.23)8  =

Probability that exactly 5 drive to work alone:  8C5·(0.77)5·(0.23)3  =

Probability that at most 4 drive to work alone:  [this would be either 4 or 3 or 2 or 1 or none of them]

=   8C4·(0.77)4·(0.23)4  +  8C3·(0.77)3·(0.23)5  +  8C2·(0.77)2·(0.23)6  +  8C1·(0.77)1·(0.23)7  +  8C0·(0.77)0·(0.23)8   =

Apr 15, 2020