Question

According to an​ article, 37​% of adults have experienced a breakup at least once during the last 10 years. Of 9 randomly selected​ adults, find the probability that the​ number, X, who have experienced a breakup at least once during the last 10 years is a. exactly​ five; at most​ five; at least five. b. at least​ one; at most one. c. between two and four​, inclusive. d. Determine the probability distribution of the random variable X. a. The probability that exactly five adults have experienced a breakup at least once during the last 10 years is nothing. ​(Round to four decimal places as​ needed.) The probability that at most five adults have experienced a breakup at least once during the last 10 years is nothing. ​(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 nothing. ​(Round to four decimal places as​ needed.) b. The probability that at least one adult has experienced a breakup at least once during the last 10 years is nothing. ​(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 nothing. ​(Round to four decimal places as​ needed.) c. The probability that between two and four ​adults, inclusive, have experienced a breakup at least once during the last 10 years is nothing. ​(Round to four decimal places as​ needed.) d. Complete the table below to determine the probability distribution of X. x Upper P left parenthesis Upper X equals x right parenthesis x Upper P left parenthesis Upper X equals x right parenthesis 0 nothing 5 nothing 1 nothing 6 nothing 2 nothing 7 nothing 3 nothing 8 nothing 4 nothing 9 nothing ​(Round to four decimal places as​ needed.) Enter your answer in each of the answer boxes.

Answer 1

a)

probability that exactly five adults have experienced a breakup at least once during the last 10 years is =⁹C₅(0.37)⁵(0.63)⁴ =0.1376

The probability that at most five adults have experienced a breakup at least once during the last 10 year =P(X<=5)=0.9304

The probability that at least five adults have experienced a breakup at least once during the last 10 years is=P(X>=5)=0.2072

b)

. The probability that at least one adult has experienced a breakup at least once during the last 10 years=1-0.63⁹ =0.9844

probability that at most one adult has experienced a breakup at least once during the last 10 years is =0.0983

c) . The probability that between two and four ​adults, inclusive, have experienced a breakup at least once during the last 10 years =P(2<=X<=4)=0.6945

d)

x	P(x)
0	0.0156
1	0.0826
2	0.1941
3	0.2660
4	0.2344
5	0.1376
6	0.0539
7	0.0136
8	0.0020
9	0.0001