The table below shows the number of marbles of different colors in a box. A fair coin is shown below the table.
Color of Marble Number
Red 10
Blue 1
Green 5
Pink 4
A coin
Dan selects a marble from the box randomly without looking and then tosses the fair coin. What is the probability that Dan will select a blue marble and the coin will land tails up?
1 over 40
3 over 40
11 over 20
19 over 20
To find the probability that Dan will select a blue marble and the coin will land tails up, we need to determine the total number of possible outcomes and the number of favorable outcomes.
The total number of possible outcomes is the product of the number of marbles and the number of coin toss outcomes. In this case, there are 4 different marbles and 2 possible coin toss outcomes (heads or tails), so the total number of possible outcomes is 4 * 2 = 8.
Now, let's determine the number of favorable outcomes. Since we want Dan to select a blue marble and the coin to land tails up, there is only 1 blue marble and 1 coin toss outcome that satisfies both conditions.
Therefore, the number of favorable outcomes is 1.
To calculate the probability, we divide the number of favorable outcomes by the total number of possible outcomes:
Probability = Number of Favorable Outcomes / Total Number of Possible Outcomes
Probability = 1 / 8
Simplifying the fraction, we get:
Probability = 1/8 = 1/2 * 1/4 = 1/2 * 1/2 * 1/2 = 1/2^3 = 1/8
So, the probability that Dan will select a blue marble and the coin will land tails up is 1/8.
Therefore, the correct answer is 1 over 8.
Please help Ms. Sue!
20 marbles, 1 blue
So, P(blue,tails) = 1/20 * 1/2 = 1/40