3.2 Classical probability practice (binomial)

(Calculator) Which one of these three events have the highest probability of occurring?

(Calculator) Darren rolls a fair cube 10 times. What is the probability of the following outcomes?

(a) There are exactly 6 even and 4 odd rolls

(b) There are at least 3 rolls that are 6s

(c) Somewhere in the 10 rolls, there are exactly 6 consecutive 1s in a row?
(A) [math]\dfrac{1296}{6^{10}}[/math]
(B) [math]\dfrac{4860}{6^{10}}[/math]
(C) [math]\dfrac{6480}{6^{10}}[/math]
(D) [math]\dfrac{8640}{6^{10}}[/math]

(Calculator) Ms. Tarr has two bags of candy. Bag A contain a mixture of 40% gummy bears and 60% jelly beans. Bag B contain a mixture of 15% gummy bears and 85% jelly beans. In a separate bowl, Ms. Tarr created a mixture using 75% from bag A and 25% from bag B.

(a) If you select a piece of candy selected at random from the bowl, what is the probability that it is a jelly bean?

(b) If you select 10 pieces of candy at random from the bowl (with replacement), what is the probability that you selected at least 7 jelly beans and that the first piece you selected was a gummy bears?

(c) Ms. Tarr wants to create a new mixture that contains 32% gummy bears. What percent of each bag did Ms. Tarr use to create this mixture?

(Calculator) A pizza cut into 8 slices. 10 slices of pepperoni are randomly placed on the pizza. When you randomly select a slice of pizza, what is the probability of taking a slice that contains no more than 2 slices of papperoni?

25% of us (humans) are unable to taste the bitter flavor of common foods such as raw broccoli, cabbage, coffee and dark beers. If you pick 5 people at random, what is the probability that: (3 decimal places)

(a) None of them taste bitter foods?

(b) Exactly 1 of them tastes bitter foods?

(c) Exactly 2 of them tastes bitter foods?

(d) That at least one of them does not taste bitter foods?