1-Many universities require a student to take a math placement test as well as computer science placement test.80% of the students who take both tests pass either the math placement test or the computer science placement test.60% pass the math placement test and 40% pass the computer science placement test.What is the probability that a student will pass both?
P(AandB)= P(A) + P(B)= .060/.080+.040/.080
=1.25

2-The following table gives the blood type and severity of a disease for a group of patients at a hospital:
BlodType
Disease Severity A B O AB
Severe 15 5 20 3
Not Severe 65 15 80 12
one of the patient records is randomly selected.
a) If the patient has a severe case of the disease,what is the probability that the patient's blood type is either B or AB?
b)If the patient has either type A or type Oblood,what is the probability that the disease is severe?
c) What is the probability that the patient's blood type is either B or AB?

a)P(AorB)=P(A)+P(B)= 5/43 + 3/43= 0.186
b)P(AorB)=P(A)+P(B)= 15/43+20/43=0.814
c)P(AorB)=P(A)+P(B)=20/215+15/215=0.162

3)A carnival game played by 682 individuals has a prize distribution that is shown in the following table:
Grand Prize 2
Large Prize 29
Small Prize 189
Consolation Prize 462

a) What is the probability of winning the large or small prize on one play of the game?
B)What is the probability of winning the small or consolation prize on one play of the game?

Would you please explain to me how to do this problem.

4) Eventa A and B have the following probabilities: P(A)=0.35, P(B)=0.45, and P(B/A)=0.50
a) Find the probability of the event A and B
P(AandB)= P(A) * P(B) = 0.35* 0.50=0.175
b) Find the probability of the event A or B
P(AorB)=P(A)+P(B)-P(AandB)= 0.35+0.45-0.175=0.625

5) Five cards are dealt from a standard deck of 52. Find the probability that they are all clubs.

Would you please explain to me the answer.
Thank you vey much

1) use the equation:
P(C or M) = P(M) + P(C) - P(C and M)

2b) = 35/180

3a) (# large + # small) / total prizes
3b) (# consolation + # small) / total prizes

in #4, answers are right, but formula in (a) isn't correct
4a) P(A and B) = P(A) * P(B|A)

5) here you'll multiply 5 things together
P(1st card is clubs) = 13/52 = 1/4
P(2nd card is clubs, given that 1st card is clubs) = 12/51
P(3rd is clubs, given 1st and 2nd are clubs) = 11/50
and so on......

:) Thank you................