I need help on this problem Please show steps on how you did

I need help on this problem. Please show steps on how you did this problem

1. P(A)=0.52, P(B)=0.38 and P(AandB)=0.10

P(B?A)=?

2. Suppose a jar contains 9 red marbles and 30 blue marbles. If you reach in the jar and pull out 2 marbles at random, what is the probability that both are red?

3. Jennifer buys a bag of cookies that contains 8 chocolate chip cookies, 7 peanut butter cookies, 5 sugar cookies and 7 oatmeal cookies. What is the probability that Jennifer randomly selects a chocolate chip cookie from the bag, eats it, then randomly selects an oatmeal cookie? Express you answer as a reduced fraction.

4. In a large population, 54 % of the people have been vaccinated. If 3 people are randomly selected, what is the probability that AT LEAST ONE of them has been vaccinated? (Give your answer as a decimal (to at least 3 places) or fraction)

5. Every cereal box has a gift inside, but you cannot tell from the outside what the gift is. The store manager assures you that 18 of the 57 boxes on the shelf have the secret decoder ring. The other 39 boxes on the shelf have a different gift inside. If you randomly select two boxes of cereal from the shelf to purchase, what is the probability that BOTH of them have the secret decoder ring? (Give answer as a decimal correct to at least three decimal places.)

Probability=

Solution

1.

p(B/A) = p(AandB)/p(A) =0.1/0.52 = 0.1923

2.

9C2 / (39C2) = (9*4) /(39*19) = 0.0486

3,

total items initially = 27

probability that Jennifer randomly selects a chocolate chip cookie from the bag, eats it = 8C1/27C1 = 8/27

then randomly selects an oatmeal cookie = (8/27)*(7C1/26C1) = 0.798

4.

out 0f 100 , 54 are vaccinated

probability that AT LEAST ONE of 3 selected at random has been vaccinated = 54C3 / (100C3) = 0.1534

5.

probability that BOTH of 2 randomly selected boxes have the secret decoder ring = 18C2 / (57C2) = 0.096