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.
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 =