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A bag contains 16 blue marbles, 12 red marbles, and 12 green marbles. If Malik randomly draws a marble from the bag (and puts it back) 25 times, how many times should he expect to pull a blue marble?

Michael draws a card from a standard deck of 52 cards (and puts it back) 20 times.
How many times can Michael expect to draw a diamond?

Wanda spun a spinner 30 times, and the results were recorded in the following tally chart.


Striped:12
Solid:9
Dotted:9

Based on the experiment, what is the probability of landing on the solid section of the spinner?
Enter your answer as a fraction, like this: 42/53

1 answer

To find the expected number of times Malik pulls a blue marble, we first need to calculate the total number of marbles in the bag:

  • Blue marbles: 16
  • Red marbles: 12
  • Green marbles: 12

Total number of marbles = 16 + 12 + 12 = 40

Now we can find the probability of drawing a blue marble:

Probability of blue marble = Number of blue marbles / Total number of marbles = 16 / 40 = 2 / 5

Malik draws a marble 25 times, so the expected number of blue marbles he pulls is given by:

Expected number of blue marbles = Probability of blue marble × Number of draws = (2/5) × 25 = 10

So, Malik should expect to pull a blue marble 10 times.

Next, for Michael drawing a diamond from a standard deck of 52 cards, we know there are 13 diamonds in the deck. The probability of drawing a diamond is:

Probability of diamond = Number of diamonds / Total number of cards = 13 / 52 = 1 / 4

Michael draws a card 20 times, so the expected number of diamonds he draws is given by:

Expected number of diamonds = Probability of diamond × Number of draws = (1/4) × 20 = 5

Therefore, Michael can expect to draw a diamond 5 times.

For Wanda's spinner, we calculate the total number of spins recorded:

Total number of spins = Striped + Solid + Dotted = 12 + 9 + 9 = 30

Now we find the probability of landing on the solid section:

Probability of landing on solid = Number of solid sections / Total spins = 9 / 30 = 3 / 10 (after simplification)

So, the probability of landing on the solid section of the spinner is 3/10.