4 There are 3 defective items in a collection of 10 items. A\"mpleof8items slate

Question

4 There are 3 defective items in a collection of 10 items. A"mpleof8items slated randomly from the group. Let the random variabe theumber of defective itema in the sample. Construct the probability mass funetion (pmb for X s. att handlers acount fr about 12% of the general ulation. (a) In a random eample of 20 people, what ia the probebdlity the there will be exnetly 3 left handers? (b) What is the probability that exnctly 30 people seed to be randomly selected to obeerve exactly 3 left handers? 6·There are 50 women and 10 men on a bus trip. Five people are randnly selected to receive door prizes. Le the random variable X be the number of men who receive a prize (a) What is the probability mass function for X? (e) What is the probability that at least one man roeives a prie? 7. Which is more likely: 6 heads in 10 tosses of a coin; or exactly 10 heads in 20 tosses? Or are they equally likely? Assume Pheada)-5. Explain your answer carefully

Explanation / Answer

Left handers account for 12% of the population; p = probability of a person being a left hander = 12/100 = 0.12
q= 1-p = probability of a person not being a left hander = 1-0.12 = 0.88

Probability of finding exactly 3 left handers in a random sample of 20 people :
applying binomial theorem for probability we get:
20C3 * p3 * q20-3 = 20*19*18/(3*2) * (0.12)3 * (0.88)17 = 1140 * 0.001728 * 0.113817 = 0.2242
So, probabaility of finding exactly 3 left handers in a random sample of 20 people ~= 0.2242

Related Questions

Navigate

• Browse (All)
• Browse 4
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.