1. Paul collects baseball cards. He has 10 outfielders, 7 pitchers, 3 managers, and 5 infielders. If he grabs a card at random, what is the probability that he will grab an outfielder card?
a. 144
b. 216
c. 8
d. 72
2. If Hank flips one coin and rolls two dice, how many permutations are possible?
a. 2/5
b. 1/5
c. 10/27
d. 2/27
Help me please!
Sure! Let's break down the problems step by step and find the solutions.
1. To find the probability of grabbing an outfielder card, we need to calculate the ratio of the number of outfielders to the total number of cards.
The total number of cards is the sum of outfielders, pitchers, managers, and infielders:
Total number of cards = 10 (outfielders) + 7 (pitchers) + 3 (managers) + 5 (infielders) = 25.
So the probability of grabbing an outfielder card is given by:
Probability = (Number of outfielder cards / Total number of cards)
Probability = 10 / 25
Simplifying, we have:
Probability = 2 / 5
Therefore, the answer is option a. 2/5.
2. To calculate the number of permutations, we need to multiply the possible outcomes of each event.
For flipping a coin, there are two possible outcomes: heads or tails.
For rolling two dice, we need to find the number of possible outcomes when rolling each die separately. Since each die has six faces, the number of outcomes for rolling two dice is 6 × 6 = 36.
To find the total number of permutations, we multiply the number of outcomes for each event:
Number of permutations = 2 (coin outcomes) × 36 (dice outcomes)
Simplifying, we have:
Number of permutations = 72
Therefore, the answer is option d. 72.
I hope that helps! Let me know if you have any further questions.