Probability and Combinations Quiz

A coin is tossed and then the spinner is spun. Determine the probability that you toss Heads and spin a Red.

• 1/6

• 1/10

• 0

• 1/12

Answer explanation

The probability of tossing Heads is 1/2, and the probability of spinning a Red is 1/3. Multiplying these probabilities gives 1/6, which is the probability of tossing Heads and spinning a Red.

What is the probability of drawing a 1, then drawing a 6? (no replacement--dependent event)

• 6/56 = 3/28

• 3/7

• 2/8 = 1/4

• 8/56 = 1/7

Answer explanation

To calculate the probability of dependent events, multiply the individual probabilities. P(1) = 1/8, P(6 after drawing 1) = 1/7. Therefore, P(1 and then 6) = (1/8) * (1/7) = 1/56 = 3/28.

Two dice are rolled. What is the probability that the sum of the numbers on the two dice will be 7?

Answer explanation

When rolling two dice, there are 6 possible outcomes that sum up to 7: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1). Out of 36 total outcomes, the probability is 1/6.

A bag contains 3 red marbles, 5 blue marbles, and 2 green marbles. If two marbles are picked at random, what is the probability that both are blue?

In a class of 30 students, there are 18 girls and 12 boys. If a group of 4 students is selected at random, what is the probability that all selected students are girls?

A password consists of 3 letters followed by 3 digits. How many different passwords can be formed if the letters must be distinct and the digits must be distinct?

• 17,160

• 15,600

• 26,280

• 46,656

A coin is flipped three times. What is the probability of getting exactly two heads?

Answer explanation

To calculate the probability of getting exactly two heads in three coin flips, we use the combination formula: C(3,2) = 3. The total number of outcomes is 2^3 = 8. Therefore, the probability is 3/8.

A jar contains 10 red, 8 blue, and 12 green marbles. If three marbles are picked at random, what is the probability that they are all of different colors?

Answer explanation

The probability of picking marbles of different colors is calculated by (10/30) * (8/29) * (12/28) = 720/1450.

What is the probability of drawing an ace from a standard deck of 52 playing cards?

Answer explanation

The probability of drawing an ace from a standard deck of 52 playing cards is 4/52 because there are 4 aces in a deck of 52 cards.

If 5 people are seated in a row, how many different ways can they be arranged?

• 120

• 60

• 24

• 720

Answer explanation

There are 5 people, so 5! (5 factorial) ways to arrange them. 5! = 5x4x3x2x1 = 120. Therefore, there are 120 different ways to arrange the 5 people in a row.