Can you help me with these Algebra 2 equations?

Question

1. If you guess the numbers at random, what is the probability of getting at least three answers correct on a five question true-false quiz. (Please show your work)

2. A caterer knows that, on average, there will be at least one broken egg in every 3 cartons. A carton contains 12 eggs. The caterer plans to serve 1200 eggs for breakfast. What is the best estimate for the number of cartons the caterer should buy :

a) 97 cartons

b) 100 cartons

c) 103 cartons

d) 112 cartons

(please explain (its either c or d)

Answer 1

1. ANSWER is 0.5

Why??

P(x ≥ 3) = BINOMIAL PROBABILITY AT LEAST 3 OF 5

P = n! / [r! * (n - r)!] * p^r - (1 - p)^(n - r)

n = TRIALS [5]

r = SUCCESSUES [3, 4, 5]

p = PROBABILITY OF SUCCESS [0.5] (true/false each question is 50% probability)

2. ANSWER:  c) 103 cartons

Why??

CARTON BUY QUANTITY = (CARTON / [# EGGS PER CARTON]) * [#EGGS NEEDED]

# EGGS PER CARTON = (12 * 3 - 1)/3 = 11.6667

CARTON BUY QUANTITY = 1/11.6667 * 1200 = 103 (rounded up)