7. a video game designer is building an algorithm that will randomly select your character’s default…

7. a video game designer is building an algorithm that will randomly select your character’s default clothing – shirt and pants. the probability of your character getting a red shirt is 0.36. the probability of your character getting black pants is 0.44. the probability of your character getting a black shirt is 0.12. the probability of your character getting white pants is 0.08. these are all independent events. a. what is the probability that your character gets both a red shirt and black pants? b. what is the probability that your character gets both a red shirt and white pants? c. what is the probability that your character gets both a black shirt and white pants? d. what is the probability that your character gets either white pants or black pants?

7. a video game designer is building an algorithm that will randomly select your character’s default clothing – shirt and pants. the probability of your character getting a red shirt is 0.36. the probability of your character getting black pants is 0.44. the probability of your character getting a black shirt is 0.12. the probability of your character getting white pants is 0.08. these are all independent events. a. what is the probability that your character gets both a red shirt and black pants? b. what is the probability that your character gets both a red shirt and white pants? c. what is the probability that your character gets both a black shirt and white pants? d. what is the probability that your character gets either white pants or black pants?

Answer

Explanation:

Step1: Recall probability - multiplication rule for independent events

For two independent events (A) and (B), (P(A\cap B)=P(A)\times P(B)).

Step2: Calculate probability for part a

Let (A) be the event of getting a red - shirt with (P(A) = 0.36), and (B) be the event of getting black pants with (P(B)=0.44). Then (P(A\cap B)=0.36\times0.44 = 0.1584).

Step3: Calculate probability for part b

Let (A) be the event of getting a red - shirt with (P(A) = 0.36), and (B) be the event of getting white pants with (P(B)=0.08). Then (P(A\cap B)=0.36\times0.08 = 0.0288).

Step4: Calculate probability for part c

Let (A) be the event of getting a black - shirt with (P(A) = 0.12), and (B) be the event of getting white pants with (P(B)=0.08). Then (P(A\cap B)=0.12\times0.08 = 0.0096).

Step5: Calculate probability for part d

For two mutually - exclusive events (C) (getting white pants) and (D) (getting black pants), (P(C\cup D)=P(C)+P(D)). Since (P(C) = 0.08) and (P(D)=0.44), then (P(C\cup D)=0.08 + 0.44=0.52).

Answer:

a. (0.1584) b. (0.0288) c. (0.0096) d. (0.52)