Question

all year

1. marli gets to choose one sweet treat and one salty treat from the choices shown.

sweet treats
chocolate bar
sugar cookie
lollipop
salty treats
popcorn
pretzels
chips
if marli randomly chooses one sweet treat and one salty treat, what is the probability that she will choose a lollipop and popcorn?

1. what is the probability of drawing a white marble from a bag containing 8 black marbles and 12 white marbles and drawing a black card from a standard deck? write your answer in decimal form.
2. what is the probability of spinning the spinner twice and landing on purple both times?
3. katie ran $2\frac{1}{4}$ miles in 30 minutes. if she continues at this rate, how long will it take katie to run $6\frac{3}{4}$ miles?

Explanation:

Problem 3

Step1: Count total sweet treats

There are 3 sweet treats: Chocolate bar, Sugar cookie, Lollipop. Probability of choosing lollipop: $\frac{1}{3}$

Step2: Count total salty treats

There are 3 salty treats: Popcorn, Pretzels, Chips. Probability of choosing popcorn: $\frac{1}{3}$

Step3: Multiply the two probabilities

For independent events, multiply individual probabilities.
$\frac{1}{3} \times \frac{1}{3} = \frac{1}{9}$

Step1: Calculate total marbles

Add black and white marbles.
$8 + 12 = 20$

Step2: Find probability of white marble

Divide white marbles by total marbles, convert to decimal.
$\frac{12}{20} = 0.6$

Step1: Probability of 1 purple spin

Spinner has 4 equal sections. Probability of purple: $\frac{1}{4}$

Step2: Probability of two purple spins

Multiply probability of one purple spin by itself.
$\frac{1}{4} \times \frac{1}{4} = \frac{1}{16}$

Answer:

$\frac{1}{9}$

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Problem 5