Independent Events Warmup 2

There are 14 tiles with one letter from the word MATHEMATICIANS on each. You are now going to choose a letter, put it back and then choose another letter. Find the probability of choosing the letter A, and then A again.

• 3/14

• 6/14

• 9/196

• 6/196

There are 14 tiles with one letter from the word MATHEMATICIANS on each. You are now going to choose a letter, put it back and then choose another letter. Find the probability of choosing the letter M, and then the letter A.

• 3/98

• 3/196

• 2/7

• 3/14

There are 14 tiles with one letter from the word MATHEMATICIANS on each. You are now going to choose a letter, put it back and then choose another letter. Find the probability of choosing a vowel, and then NOT the letter T.

• 18/196

• 36/196

• 18/49

• 8/14

Answer explanation

To find the probability, first calculate the total vowels (6) and non-T consonants (5) out of 14. Probability = (6/14) * (5/13) = 18/49.

A bag contains 8 blue marbles, 7 green marbles, and 5 yellow marbles. Suppose you drew one marble from the bag above, replaced it and then drew a second marble. What is the probability of picking a yellow marble, and then blue? P(yellow, blue)

• 9/20

• 3/20

• 1/10

• 13/20

Answer explanation

This is an example explanation.

A bag contains 8 blue marbles, 7 green marbles, and 5 yellow marbles. Suppose you drew one marble from the bag above, replaced it and then drew a second marble. What is the probability of picking a non-blue marble on both draws? P(not blue, not blue)

• 9/25

• 4/25

• 3/4

• 1/2

Answer explanation

The probability of picking a non-blue marble on the first draw is (7+5)/(8+7+5) = 12/20. The probability of picking a non-blue marble on the second draw is also 12/20. Multiplying these probabilities gives (12/20)*(12/20) = 9/25.

A bag contains 8 blue marbles, 7 green marbles, and 5 yellow marbles. Suppose you drew one marble from the bag above, replaced it and then drew a second marble. What is the probability of picking a yellow marble on both draws? P(both yellow)

• 1/10

• 9/16

• 1/4

• 1/16

Answer explanation

The probability of drawing a yellow marble on the first draw is 5/20, and the same for the second draw. Therefore, the probability of picking a yellow marble on both draws is (5/20) * (5/20) = 1/16.