Question

NO LINKS!! URGENT HELP PLEASE!!!!

Find the probability.

30. You flip a coin twice. The first flip lands heads-up and the second flip lands tails-up.

31. A cooler contains 10 bottles of sports drinks: 4 lemon-lime flavored, 3 orange-flavored, and 3 fruit-punch flavored. You randomly grab a bottle. Then you return the bottle to the cooler, mix up the bottles, and randomly select another bottle. Both times you get a lemon-lime drink.

Answer 1

Flipping a coin twice and obtaining heads the first time and tails the second time has a probability of (1/2) * (1/2) = 1/4.

On the initial draw, there is a 4/10 chance that a drink with a lemon-lime flavor will be randomly chosen from the cooler. Because the bottle is put back in the cooler and mixed before the second draw, the likelihood of choosing a lemon-lime beverage at random is also 4/10. The likelihood of winning a lemon-lime drink on both draws is (4/10) * (4/10), which equals 16/100 or 4/25.

Explanation:

Answer 2

`\textsf{30)} \quad (1)/(4)=25\%`

`\textsf{31)} \quad (4)/(25)=16\%`

Explanation:

Probability is a measure of the likelihood or chance of an event occurring. The basic formula for probability is:

`\boxed{{\sf Probability\:of\:an\:event\:occurring = (Number\:of\:ways\:it\:can\:occur)/(Total\:number\:of\:possible\:outcomes)}}`

Question 30

A fair coin has two possible outcomes: heads (H) or tails (T).

Each flip of the coin is independent, meaning the outcome of one flip does not affect the outcome of the other flip.

The probability of flipping a head is P(H) = 1/2.

The probability of filliping a tail is P(T) = 1/2.

To find the probability that the first flip lands heads-up and the second flip lands tails-up, we multiply the individual probabilities together:

`\sf P(H)\;and\;P(T)=(1)/(2) \cdot (1)/(2)=(1 \cdot 1)/(2 \cdot 2)=(1)/(4)`

So the probability of flipping a coin twice and getting heads on the first flip and tails on the second flip is 1/4 or 25%.

`\hrulefill`

Question 31

There are 10 bottles in total, so there are 10 possible outcomes.

There are 4 lemon-lime drinks in the cooler, therefore the probability of selecting a lemon-lime bottle is:

`\sf P(lemon$-$\sf lime)=(4)/(10)`

As you are randomly selecting two bottles with replacement, meaning you return the bottle to the cooler before selecting the next one, the probability of selecting a lemon-lime bottle each time is the same.

To find the probability of that both drinks are lemon-lime flavored, multiply the individual probabilities together:

`\begin{aligned}\sf Probability &= \textsf{P(lemon-lime)} \cdot \textsf{P(lemon-lime)}\\\\&= (4)/(10) \cdot (4)/(10)\\\\&=(4 \cdot 4)/(10 \cdot 10)\\\\&=(16)/(100)\\\\&=(4)/(25)\end{aligned}`

Therefore, the probability of randomly selecting two drinks from the cooler and getting a lemon-lime drink both times is 4/25 or 16%.