In a Internee program at Airline Company, 60 percent of the internees are female and 40 percent male. 80 percent of the females are business students, and 65 percent of the males are business students.
a) An internee is selected at random. What is the probability that the person selected is a female
who is not a business student?
b) Are gender and field of study, independent in this case? Why?
Part – B: Marks [2]
A firm purchases a microchip used in the manufacturing of LED screens from four different suppliers. TechZone supplies 30 percent of the total microchips, Advance Electronics 25 percent, PSP importers 18 percent, and TechParts inc. 32 percent. TechZone tends to have the best quality, as only 3 percent of its microchips arrive defective. Advance Electronics chips are 4 percent defective, PSP importers chips are 7 percent defective, and Parts Inc. are 6.5 percent defective.
a) If a random chip is selected, what is the probability that the chip is defective
b) A defective chip was discovered in the latest shipment. What is the probability that it came
from TechZone supplies?
c) A defective chip was discovered in the latest shipment. What is the probability that it came
from Parts Inc.?
Page 6 of 7
Part – C: Marks [2]
Pakistan Cricket Board in its central contract places its International players in four different categories, Category A, Category B, Category C and Emerging Players’ Category. Batsmen who are going to play in upcoming series fall into these four categories in the proportions 30 percent, 40 percent, 20 percent and 10 percent. The probability that a Category A player will get out without scoring a single run is 0.01, for Category B player its 0.04, for Category C player its 0.12 and the probability that an emerging player will get out on Zero is 0.06.
During a match after the fall of second wicket captain sent Muhammad Rizwan on batting and he got out on Zero. What is trhe probability that Muhammad Rizwan is;
a) In Category A
b) In Category B
c) In Category C
Answers
Answer:
loading but bahot hard
Do as follows
Explanation:
PART A- Internee program at Airline Company
Construct a contingency table from the information given
Gender/field of study Business non-business Total
Male 0.65 * 40 = 26 14 40
Female 0.80 * 60 = 48 12 60
Total 74 26 100
a) An internee is selected at random. What is the probability that the person selected is a female who is not a business student?
P (female but not business student)
= 12/100
= 0.12
b) Are gender and field of study, independent in this case? Why?
Gender & field of study are not independent.
condition for independent events:
P (A and B) = P(A) * P(B)
so for instance, P (female & business student) = 48 / 100 = 0.48
P (female) P (business student)
= 60 / 100 * 74 / 100
= 0.444
As they are not equal, we say that "gender & field of study are not independent"
PART B -Techzone supplies
A denote the event that chip came from TechZone,
BBB denote the event that chip came from Advance Electronics,
CCC denote the event that chip came from PSP,
FFF denote the event that chip came from Parts Inc, and
DDD denote the event that the randomly selected chip is defective.
Given
P(A)=0.30, P(D/A)=0.03,
P(B)=0.25, P(D/B)=0.04,
P(C)=0.18, P(D/C)=0.07,
P(F)=0.32, P(D/F)=0.065.
a) If a random chip is selected, what is the probability that the chip is defective
b) A defective chip was discovered in the latest shipment. What is the probability that it came from TechZone supplies?
We apply Bayes' Theorem to compute this probability
c) A defective chip was discovered in the latest shipment. What is the probability that it came from Parts Inc.?
We apply Bayes' Theorem to compute this probability
P(F/D)= P (F) P (D/F) / P (D)
= 0.32 (0.065) / 0.05240
= 52/131
= 0.3969
PART C - Pakistan Cricket Board
P (A) = 0.30
P (B) = 0.40
P (C) = 0.20
P (Emerging) = 0.10
P (without scoring/A) = 0.01
P (without scoring/B) = 0.04
P (without scoring/C) = 0.12
P (without scoring/Emerging) = 0.06
What is the probability that Muhammad Rizwan is; a) In Category A
P = P(A) * P(without scoring/A) / (P(A)*P(without scoring/A) + P(B)*P(without scoring/B) + P(C) *P (without scoring/C) + P (Emerging) * P (without scoring/Emerging))
= (0.30*0.01) / (0.30*0.01 + 0.40*0.04 + 0.20*0.12 + 0.10*0.06)
= 0.003/0.049
= 0.061
What is the probability that Muhammad Rizwan is; a) In Category B
P=P(B) * P (without scoring/B) / (P(A) * P (without scoring/A) + P(B) * P (without scoring/B) + P (C) * P (without scoring/C) + P(Emerging) * P (without scoring/Emerging))
= (0.30*0.01) / (0.30 *0.01 + 0.40*0.04 + 0.20 *0.12 + 0.10 *0.06)
= 0.016/0.049
= 0.3265
What is the probability that Muhammad Rizwan is; a) In Category B
P=P(C) * P (without scoring/C) / (P(A) * P (without scoring/A) + P (B) * P (without scoring/B) + P(C) * P (without scoring/C) + P(Emerging) * P (without scoring/Emerging))
= (0.30*0.01) / (0.30*0.01 + 0.40*0.04 + 0.20*0.12 + 0.10*0.06)
= 0.024/0.049
= 0.49
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