The probability of a certain baseball player hitting a foul ball is one-fourth. How many foul balls would you expect her to hit after 80 swings?
A. 4
B. 20
C. 40
D. 60
The probability of hitting a foul ball on a single swing is 1/4. So, on average, we expect her to hit 1/4 foul balls for every swing. Using this information, we can find out how many foul balls we would expect her to hit after 80 swings:
Expected number of foul balls = Probability of hitting a foul ball x Number of swings
Expected number of foul balls = 1/4 x 80
Expected number of foul balls = 20
Therefore, we would expect her to hit 20 foul balls after 80 swings.
The answer is B. 20.
A true-false test has 8 questions. What is the probability of guessing the correct answers to all of the questions?
A. one-tenth
B. Start Fraction 1 over 16 End Fraction
C. Start Fraction 1 over 64 End Fraction
D. Start Fraction 1 over 256 End Fraction
For each question, the probability of guessing the correct answer is 1/2, since there are only two options: true or false. To find the probability of guessing all 8 correctly, we need to multiply the probabilities of each individual guess:
P(guessing all 8 correctly) = (1/2) x (1/2) x (1/2) x (1/2) x (1/2) x (1/2) x (1/2) x (1/2)
Simplifying this expression, we get:
P(guessing all 8 correctly) = (1/2)^8
To convert this to a fraction, we can write:
P(guessing all 8 correctly) = 1/ (2^8)
2^8 = 256, so this can be simplified further:
P(guessing all 8 correctly) = 1/256
Therefore, the answer is D. Start Fraction 1 over 256 End Fraction.
are you sure?
Yes, I am sure. The probability of guessing all 8 questions correctly on a true-false test when guessing randomly is very low. The probability can be calculated as shown above, and it comes out to be 1/256.
Simplify 4!
A. 24
B. 10
C. 9
D. 4
4! means 4 factorial, which is equal to:
4! = 4 x 3 x 2 x 1
Multiplying these numbers, we get:
4! = 24
Therefore, the answer is A. 24.