Answer:
9.
The probabilities are the same
10.
1/3
Step-by-step explanation:
9.
Assuming the coin is fair;
The probability of getting heads in a single toss is, P(H) = 1/2
The probability of getting tails in a single toss is, P(T) = 1/2
Now, P(H,H,H) is the probability of obtaining 3 heads in the e tosses. Since each toss is independent of the others,;
P(H,H,H) = P(H)*P(H)*P(H)
= 1/2 * 1/2 * 1/2 = 1/8
On the other hand, P(H,T,H) is the probability of obtaining a head followed by a tail followed by a final head. Using the independence property;
P(H,T,H) = P(H)*P(T)*P(H)
= 1/2 * 1/2 * 1/2 = 1/8
Therefore, P(H,H,H) = P(H,T,H)
10.
We are informed that a coin is tossed and a number cube is rolled. We are to determine the following probability;
P(heads, a number less than 5)
Assuming the coin is fair;
The probability of getting heads in a single toss is, P(H) = 1/2
Assuming the number cube is fair as well, the probability of rolling a number less than 5 is;
4/6 = 2/3
This is because there are 4 numbers less than 5, (1, 2, 3, 4) while the cube has 6 sides.
P(heads, a number less than 5), the events presented here are independent since the outcome from tossing the coin does not in any way determine the outcome from rolling the number cube. Therefore,;
P(heads, a number less than 5) = P(heads)*P(a number less than 5)
= 1/2 * 2/3 = 1/3
and use algebra to prove the statement.
. Multiply this by ten to get 
. Subtract the initial equation to give 
and divide by 
to see that 
. Substituting into the original equation gives