Probability — Quiz 2

Questions in this quiz (6)

1. Carlos is creating a 12-character password. He must use exactly six vowels (A, E, I, O, U, and Y) and six consonants (B, C, D, F, G, H, J, K, L, M, N, P, Q, R, S, T, V, W, X, Z). Additionally, Carlos ensures that no two vowels are consecutive, and no two consonants are consecutive. How many different passwords can Carlos create following these rules?

   • $$(6^2)!$$
   • $$2! \times 6! \times 20!$$
   • $$20 \times 6! \times 2!$$
   • $$2 \times 6! \times 20!$$

2. In how many distinct ways can 6 people stand in a line with 2 ends?

   • 240
   • 180
   • 720
   • 120

3. In a round-robin table tennis tournament, each participant played every other participant exactly twice. If there were 10 players, how many games were played?

   • 100
   • 90
   • 50
   • 101

4. As part of a science experiment, Alex flips a fair coin 5 times. What is the probability of getting exactly 3 heads?

   • $$\frac{1}{2}$$
   • $$\frac{5}{32}$$
   • $$\frac{5}{16}$$
   • $$\frac{1}{16}$$

5. If a basketball team has a 70% chance of winning each of three games, and the games are independent events, what is the probability that the team loses all three games?

   • $$0.3%$$
   • $$2.7%$$
   • $$3%$$
   • $$27%$$

6. If Sarah rolls two standard six-sided dice, what is the probability that the sum of the numbers on the dice is exactly 10?

   • $$\frac{1}{12}$$
   • $$\frac{1}{36}$$
   • $$\frac{1}{3}$$
   • $$\frac{5}{6}$$