PLEASE HELP!!!! A bag contains 1 white (W), 3 blue (B1, B2, B3), and 2 red (R1, R2) marbles. (4 points)
a. Use a tree diagram to list all the possible outcomes for tossing a coin and then drawing a marble from the bag.
b. Are these independent or dependent events?
c. Find the probability of tossing a head and drawing a red marble. Explain your reasoning.
d. Find the probability of drawing two blue marbles if the first marble is not replaced. Explain your reasoning.

Answers

Answer 1

The answers are as follows:

a. There are 6 ways of tossing a coin and then drawing a marble from the bag. (Tree diagram is shown in the diagram below) The probability is 1/12.

b. These are independent events since tossing a coin does not affect the drawing of marble from the bag.

c. From the tree diagram, the probability of tossing a head and drawing a red marble is 1/6(since they are independent events).

d. The probability of drawing two blue marbles if the first marble is not replaced is 1/5(since they are dependent events).

What are compound events in probability?Two or more events that occur simultaneously or one after the other are said to be compound events. They are calculated by multiplying the probability of the first event by the probability of the second event.

Calculation:

It is given that a bag contains,

Number of white marbles(W) = 1

Number of Blue marbles (B) = 3

Number of Red marbles (R) = 2

Thus, there are 6 marbles in the bag. So, the sample space for drawing a marble = 6

a. Finding all the possible outcomes using a tree diagram:

The possible outcomes from the tree diagram are

(H, W), (H, B), (H, R), (T, W), (T, B), and (T, R)

The probability of tossing head or tail = 1/2

The probability of drawing a marble from the bag = 1/6

So, the compound probability = (1/2)(1/6) = (1/12)

The sample space for this is 12.

b. Independent or dependent events:

These are independent events since the tossing of a coin does not affect the drawing of marble from the bag.

c. Finding the probability of tossing a head and drawing a red marble:

The probability of tossing a head = 1/2

The probability of drawing a red marble = 2/6 = 1/2

Since they are independent events,

The required probability = (1/2)(1/2) = 1/4

d. Finding the probability of drawing two blue marbles if the first marble is not replaced:

The probability of drawing a blue marble from the bag(1st attempt) = 3/6

The probability of drawing another blue marble from the bag (2nd attempt) = 2/5 (From the leftover marbles after the first attempt)

Since they are dependent events, the probability of the 2nd event is calculated only after the first event is calculated.

So, the required probability = (3/6)(2/5) = 1/5

Thus, all the probabilities are calculated.

Learn more about compound probabilities here:

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PLEASE HELP!!!! A Bag Contains 1 White (W), 3 Blue (B1, B2, B3), And 2 Red (R1, R2) Marbles. (4 Points)a.

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