Question

1) There are 6 yellow card, 3 blue cards, 4 pink cards and 7 purple cards in a hat. What is the probability of selecting a purple card, then another purple card? Give answers as reduced fraction and percent.

2) A bag of letter tiles has the following: a w r t b j y. What is the probability of selecting t, replacing it, then selecting y? Give answers as reduced fractions and percent

3) Joe spins a spinner that has five equal sections, yellow, white, orange, green and pink. He also flips a coin. 1) How many possible outcomes would there be if you drew a tree diagram? 2)What is the probability of spinning and landing on pink? 3) What is the probability of spinning and landing on red?

Answer 1

1) 21/190 = 11.05%

2) 1/49 = 2.04%

3) 1) 10 possible outcomes, 2) 1/5 = 20% for spinning on pink, 3) 1/5 = 20% for spinning on red

Explanation:

1)

We have a total of 6 + 3 + 4 + 7 = 20 cards, and from these cards 7 are purple, so the probability of selecting the first card purple is 7/20. Then, the probability of selecting the second card also purple is 6/19, because now we have 6 purple cards in a total of 19 cards.

So the final probability is (7/20) * (6/19) = 21/190 = 11.05%

2)

We have a total of 7 letters, and all of them are different. So the probability of selecting t is 1/7, and the probability of selecting y is also 1/7, as the letter is replaced after being selected.

So the final probability is (1/7) * (1/7) = 1/49 = 2.04%

3)

For the spinner we have 5 possible values, and for the coin we have 2 possible values, so the number of outcomes is the product of these number of possibilities: 5 * 2 = 10

The probability of spinning and landing on pink is 1/5 = 20%, as we have one pink option among 5 options.

The probability of spinning and landing on red is 1/5 = 20%, as we have one red option among 5 options.