Question

A According to an article, 40% of aduls have experienced a breakup at least once during the last 10 yoars. Of9 andomly selected adults, find the probability that the numbe, X, who have experienced a breakup at least onoe during the last 10 yoars is a. exactly five, at most five, at loast five. b. at least one; at most one c. between five and seven, inclusive. d. Determine the probability distribution of the random variable X a. The probabilty that exactly five aduts have experionced a breakup at leant once during the last 10 years is (Round to four decimal places as needed) The probabiity that at most five adults have axperienced a breakup at least once during the last 10 years isi (Round to four decimal places as needed) The probability that at least five adults have experienced a breakup at least once during the last 10 years is (Round to four decimal places as needed) b. The probability that at least one adult has experienced a breakp at least once during the last 10 years is (Round to four decimal places as needed) The probability that at most one adult has experienced a breakup at least once during the last 10 years is (Round to four decimal places as needed) c. The probability that betwoen five and seven aduits, inclusive, have experienced a breakup at least once during the last 10 years is (Round to four decimal places as needed.) d. Complete the table below to delermine the probability distribuion of X PIX x) POX x) fi T (Round to four decimal places as needed ) Enter your answer in each of the answer boxes MacBook 4 esc & 7 2 3

Answer 1

a)P(exactly 5 ) =⁹C₅(0.49)⁵(0.51)⁴ =0.2408

P(at most 5) =P(X<=5) =0.7654

P(at least 5) =P(X>=5)=0.4754

b)

P(at least one adult)=P(X>=1)=0.9977

P(at most 1 adult) =P(X<=1)=0.0225

c)

P(between 5 and 7) =0.4585

d)

x	P(x)		x	P(x)
0	0.0023		5	0.2408
1	0.0202		6	0.1542
2	0.0776		7	0.0635
3	0.1739		8	0.0153
4	0.2506		9	0.0016