Mathematics, 23.03.2021 01:30 hailey200127

You decide to perform an experiment with a standard deck of 52 cards and a set of 6-sideddice. You start by randomly picking a card from the deck. If the card is a diamond, you roll2 dice and record the sum of the dice. Otherwise, you roll 1 die and record the value of thedie. If you wrote down a 5, what is the probability the card you drew was a diamond

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Answer from: sbush1412

Probability of diamond card selected when 5 is write down = $\frac{2}{11}$

Step-by-step explanation:

Given - You decide to perform an experiment with a standard deck of 52 cards and a set of 6-sided dice. You start by randomly picking a card from the deck. If the card is a diamond, you roll 2 dice and record the sum of the dice. Otherwise, you roll 1 die and record the value of the die.

To find - If you wrote down a 5, what is the probability the card you drew was a diamond ?

Proof -

Total Number of cards in a deck = 52

Total number of Diamond card in a deck = 13

Now,

P(diamond card) = $\frac{13}{52}$ = $\frac{1}{4}$

P(not a diamond card) = 1 - $\frac{1}{4}$ = $\frac{3}{4}$

Now,

Total outcomes when two dice are rolled = 36

Total outcome of getting 5 when two dice are rolled = { (1,4), (2,3). (3,2), (4,1) }

So,

P(Sum 5 when two dice are rolled ) = $\frac{4}{36}$ = $\frac{1}{9}$

P(Sum 5 when one dice is rolled ) = $\frac{1}{6}$

Now,

P(sum 5 when diamond card is selected) = $\frac{1}{4}$ × $\frac{1}{9}$ = $\frac{1}{36}$

P(sum 5 when diamond card is not selected = $\frac{3}{4}$ × $\frac{1}{6}$ = $\frac{1}{8}$

Now,

Probability (Getting 5) = $\frac{1}{36}$ + $\frac{1}{8}$ = $\frac{11}{72}$

Now,

Probability of diamond card selected when 5 is write down = $\frac{\frac{1}{36} }{\frac{11}{72} }$

= $\frac{1}{36}$ × $\frac{72}{11}$ = $\frac{2}{11}$

⇒Probability of diamond card selected when 5 is write down = $\frac{2}{11}$

Answer from: Quest

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Answer from: Quest

b: |12 – x| ≤ 0.25

step-by-step explanation:

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation:

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