Question

Four percent of the tenants in an apartment building live alone. Suppose five tenants are selected randomly. What expression represents P(all live alone)?

Similarly, a survey shows that 60% of the adults floss their teeth every day. In a random sample of 10 adults, what is the probability that exactly 6 floss every day?

Answer 1

1. Since 4 % = 4/100 = 0.04, hence the probability that all the five tenants, selected randomly, live alone, is 0.04 x 0.04 x 0.04 x 0.04 x 0.04 = (0.04)⁵ = 0.000001024

2. As per the binomial binomial formula, in a random sample of 10 adults, the probability that exactly 6 adults floss every day is
¹⁰C₆* (0.6)⁶*(0.4)⁴ = (10*9*8*7)/(4*3*2*1) * 0.046656 * 0.0256 = = 5040/24 * 0.046656 * 0.0256
= 0.250823 .
Thus, the probability that exactly 6 adults floss every day is 0.25 ( on rounding off to 2 decimal places).