js bank internship report
Question 1: Suppose that vehicles taking a particular motorway exit can turn right (R), turn left (L) or go straight (S). Now consider the direction observance by each ofthe three successive vehicles.
a. List all the outcomes in the event A that all three vehicles go in the same direction.
b. List all outcomes in the event B that all three vehicles take different route direction.
c. List all outcomes in event C that exactly two of the three vehicles turn right.
d. List all the outcomes in the event D that exactly two vehicles go in the same direction.
e. List outcomes in D', C U D, C n D
Solution:
a. Outcomes in same direction: A= (LLL, RRR, SSS) (where L=left, R=Right and S=Straight)
b. Outcomes when all the three vehicles take different route direction: B= (LRS, LSR, RLS, RSL, SRL, SLR) (where L=left, R=Right and S=Straight)
c. Outcomes in which exactly two of the three vehicles turn right: C= (RRL, RLR, LRR, RRS, RSR, SRR)
d. Outcomes in which exactly two vehicles go in the same direction: D= (RRL, RLR, LRR, RRS, RSR, SRR, SSR, SRS, RSS, SSL, SLS, LSS, LLS, LSL, SLL, LLR, LRL, RLL)
e. Outcomes in D', (C D), (C D) D’= (LLL, RRR, SSS, RLS, LRS, LSR, RLS, RSL, SRL, SLR)
(C D)= (RRL, RLR, LRR, RRS, RSR, SRR, SSR, SRS, RSS, SSL, SLS, LSS, LLS, LSL, SLL, LLR, LRL, RLL)
(C D)= (RRL, RLR, LRR, RRS, RSR, SRR)
Question 2: Consider randomly selected students at a certain University, and let ‘A’ denote the event that the selected individual has a Visa Credit Card and the ‘B’ analogous event for a Master Card. Suppose that P(A)=0.5; P(B)=0.4; P(AB)=0.25
a. Compute the probability that the selected individual has at least one credit card.
b. What is the probability that the selected individual has neither type of card?
c. Describe in terms of A and B, the event that the selected student has a Visa Card but not a Master Card and then calculate the probability of this event.
Solution:
a.
a. List all the outcomes in the event A that all three vehicles go in the same direction.
b. List all outcomes in the event B that all three vehicles take different route direction.
c. List all outcomes in event C that exactly two of the three vehicles turn right.
d. List all the outcomes in the event D that exactly two vehicles go in the same direction.
e. List outcomes in D', C U D, C n D
Solution:
a. Outcomes in same direction: A= (LLL, RRR, SSS) (where L=left, R=Right and S=Straight)
b. Outcomes when all the three vehicles take different route direction: B= (LRS, LSR, RLS, RSL, SRL, SLR) (where L=left, R=Right and S=Straight)
c. Outcomes in which exactly two of the three vehicles turn right: C= (RRL, RLR, LRR, RRS, RSR, SRR)
d. Outcomes in which exactly two vehicles go in the same direction: D= (RRL, RLR, LRR, RRS, RSR, SRR, SSR, SRS, RSS, SSL, SLS, LSS, LLS, LSL, SLL, LLR, LRL, RLL)
e. Outcomes in D', (C D), (C D) D’= (LLL, RRR, SSS, RLS, LRS, LSR, RLS, RSL, SRL, SLR)
(C D)= (RRL, RLR, LRR, RRS, RSR, SRR, SSR, SRS, RSS, SSL, SLS, LSS, LLS, LSL, SLL, LLR, LRL, RLL)
(C D)= (RRL, RLR, LRR, RRS, RSR, SRR)
Question 2: Consider randomly selected students at a certain University, and let ‘A’ denote the event that the selected individual has a Visa Credit Card and the ‘B’ analogous event for a Master Card. Suppose that P(A)=0.5; P(B)=0.4; P(AB)=0.25
a. Compute the probability that the selected individual has at least one credit card.
b. What is the probability that the selected individual has neither type of card?
c. Describe in terms of A and B, the event that the selected student has a Visa Card but not a Master Card and then calculate the probability of this event.
Solution:
a.