Question

A bag contains 8 red, 4 blue, and 4 yellow marbles. What is the probability of randomly choosing 2 blue marbles without replacement? Write the answer as a decimal. Round to the nearest hundredth if needed. And What is the probability of getting heads, tails, and heads, in that order when flipping a coin? are these events dependent or independent? A. 1/8 dependent B. 1/8 independent C. 1/6 dependent D. 1/6 independent. Please help me i really need it thank you so much for whoever helps me.

Answer 1

bags = 8+4+4=16
firs step
p1=4/16
second step
p2=3/15
P=4/16*3/15=1/4*1/5=1/20=0,05 - correct answer

Answer 2

Answer: The probability of randomly choosing 2 blue marbles without replacement is
`0.05`.

B. The probability of getting heads, tails, and heads, in that order when flipping a coin is 1/8.

These events are independent.

Explanation:

Given: The number of blue marbles in the bag = 4

The total number of marbles in the bag =
`8+4+4=16`

After choosing one marble, the total marbles remains in the bag =
`16+1=15`

If first marble is blue, then number of blue marbles in bag =

Now, the the probability of randomly choosing 2 blue marbles without replacement is given by :-

`(4)/(16)*(3)/(15)=(1)/(20)=0.05`

Hence, the probability of randomly choosing 2 blue marbles without replacement is
`0.05`.

In order when flipping a coin.

Total outcomes = 2

Then, the probability of getting heads, tails, and heads, in that order when flipping a coin is given by :-

`(1)/(2)*(1)/(2)*(1)/(2)=(1)/(8)`

These events are independent of each other because the next event is not affected by the previous event.