Question

8 multiple choice 2 points the four faces of a fair tetrahedron die are numbered 1, 2, 3, and 4. in two tosses of the die, the probability of obtaining exactly two 4’s is 1/16 1/2 1/4 1/8 9 multiple choice 2 points if two coins are tossed, the probability of getting two tails is 1/2 1/8 1/4 1/3 10 multiple choice 2 points the probability of throwing two fours on a single toss of a pair of dice is 1/6 1/3 1/12 1/36

Explanation:

Step1: Recall probability formula for independent events

For independent events \(A\) and \(B\), \(P(A\cap B)=P(A)\times P(B)\).

Step2: Solve question 8

The probability of getting a 4 on a single - toss of a fair tetrahedron die is \(P = \frac{1}{4}\). Since the two tosses are independent events, the probability of getting a 4 on the first toss and a 4 on the second toss is \(P=\frac{1}{4}\times\frac{1}{4}=\frac{1}{16}\).

Step3: Solve question 9

The probability of getting a tail on a single - coin toss is \(\frac{1}{2}\). Since the two coin - tosses are independent events, the probability of getting a tail on the first toss and a tail on the second toss is \(P=\frac{1}{2}\times\frac{1}{2}=\frac{1}{4}\).

Step4: Solve question 10

The probability of getting a 4 on a single die toss is \(\frac{1}{6}\). Since the two die - tosses are independent events, the probability of getting a 4 on the first die and a 4 on the second die is \(P=\frac{1}{6}\times\frac{1}{6}=\frac{1}{36}\).

Answer:

1. \(\frac{1}{16}\)
2. \(\frac{1}{4}\)
3. \(\frac{1}{36}\)