Question

name:

1. eighteen people in a test group of 93 claimed to still have indigestion after consuming a new antacid tablet. what is the probability that the antacid will leave a person feeling better (ie. no indigestion), expressed as a decimal? 1
2. what is the probability of pulling the 3 of hearts from a deck of cards, expressed as a fraction? 1
3. a box of crayons has 5 shades of red, 4 shades of blue, 6 shades of yellow, and 3 shades of green. what is the probability of pulling a blue crayon and then a yellow crayon expressed as a fraction? 1
4. the probability of twins being born is 11 in 300. if 770 women give birth at a hospital, how many of them can be expected to have twins? 2

Explanation:

Step1: Calculate number of people feeling better

The number of people who still have indigestion is 18 out of 93. So the number of people feeling better is $93 - 18=75$.

Step2: Calculate probability

The probability $P$ that a person feels better is the number of people feeling better divided by the total number of people in the test - group. So $P=\frac{75}{93}\approx0.806$.

Step1: Identify total number of cards and favorable outcomes

A standard deck of cards has 52 cards. There is only 1 card that is the 3 of hearts.

Step2: Calculate probability

The probability $P$ of pulling the 3 of hearts is the number of favorable outcomes (1) divided by the total number of outcomes (52). So $P = \frac{1}{52}$.

Step1: Calculate total number of crayons

The total number of crayons is $5 + 4+6 + 3=18$.

Step2: Calculate probability of pulling a blue crayon first

The probability of pulling a blue crayon first is $\frac{4}{18}$.

Step3: Calculate probability of pulling a yellow crayon second

After pulling a blue crayon, there are 17 crayons left. The probability of pulling a yellow crayon second is $\frac{6}{17}$.

Step4: Calculate combined probability

The probability of pulling a blue crayon and then a yellow crayon is the product of the two probabilities. So $P=\frac{4}{18}\times\frac{6}{17}=\frac{24}{306}=\frac{4}{51}$.

Step1: Set up proportion

Let $x$ be the number of women expected to have twins. We set up the proportion $\frac{11}{300}=\frac{x}{770}$.

Step2: Cross - multiply and solve for $x$

Cross - multiplying gives $300x=11\times770$. Then $300x = 8470$. So $x=\frac{8470}{300}=\frac{847}{30}\approx28.23$. Since we are talking about the number of women, we round to the nearest whole number, $x = 28$.

Answer:

$0.806$