At a certain charity fundraiser, some guests will be randomly selected to receive a gift. The probability of receiving a gift is 3/25. Find the odds in favor of receiving a gift. I got 3/28. A child has a box of candies which might have a toy inside. The odds against the box having a toy are 7/2. What is the probability of the box having a toy? I got 7/9. Are my answers correct?

a) Your answer for part a (I got 3/28) is wrong.

Odds are always expressed as ratios after calculating. Therefore, the odds in favour of receiving a gift = 3:22

b) Your answer in part b(I got 7/9) is correct.

The probability of the box having a toy is 7/9.

Step-by-step explanation:

The question above has to do with odds and probability.

It is important to note that odds are expressed in the form of ratios while probabilities are expressed as fractions.

a) At a certain charity fundraiser, some guests will be randomly selected to receive a gift. The probability of receiving a gift is 3/25. Find the odds in favor of receiving a gift.(I got 3/28)

The formula for calculating odds from probability is Odds = Probability / (1 - Probability).

Probability = 3/25

Odds =(3/25)/(1 - 3/25)

= (3/25)/22/25

= 3/25 ÷ 22/25

= 3/25 × 25/22

= 3/22

Note that odds are always expressed as ratios.

Therefore, the odds in favour of receiving a gift = 3:22

Your answer for part a (I got 3/28) is wrong.

The correct answer is 3:22

b) A child has a box of candies which might have a toy inside. The odds against the box having a toy are 7/2. What is the probability of the box having a toy? I got 7/9.

The formula for calculating probability from odds is P = Odds / (Odds + 1).

Odds = 7/2 or 7:2

We convert the odds to fraction when calculating

Probability = Odds / (Odds + 1).

Probability = (7/2)/ (7/2 + 1)

Probability = (7/2)/9/2

Probability = 7/2 ÷ 9/2

= 7/2 × 2/9

= 7/9

Probability is always expressed as a fraction.

Therefore, the probability of the box having a toy is 7/9.

Your answer in part b(I got 7/9) is correct.

- 2 + 10x³ - 21x² + 19x - 4

step-by-step explanation:

each term in the second factor is multiplied by each term in the first factor

x²(- 2x² + 4x - 1) - 3x(- 2x² + 4x - 1) + 4(- 2x² + 4x - 1) ← distribute

= - 2 + 4x³ - x² + 6x³ - 12x² + 3x -8x² + 16x - 4

collect like terms

= - 2 + 10x³ - 21x² + 19x - 4 ← in standard form