Question

In the two oming basketball games, the probability that utc will defeat marshall is 0.63, and the probability that utc will defeat furman is 0.55. The probability that utc will defeat both opponents is 0.3465.

a. what is the probability that utc will defeat furman given that they defeat marshall?

b. what is the probability that utc will win at least one of the games?

c. what is the probability of utc winning both games?

d. are the outcomes of the games independent? Explain and substantiate your answer.

Answer 1

The probability that utc will defeat marshall, P(M)=0.63

The probability that utc will defeat furman, P(F)=0.55

The probability that utc will defeat both oponents, P(M intersection F)=0.3465

a. The probability that utc will defeat furman given that they defeat marshall= P(M intersection F)/ P(M)

= 0.3465/0.63=0.55

b. The probability that utc will win at least one of the games= P(M U F)

= P(M) + P(F) - P(M intersection F)=0.63+0.55-0.3465=0.8335

c. The probability of utc winning both games= probability of utc defeating both opponents=0.3465

d. Since the probability that utc will defeat furman given that they defeat marshall is equal to the probability of utc that utc will defeat furman, therefore, the outcomes of the games are independent.