Please check for me:
Solve the questions below and identify them as experimental or theoretical.
a. A baseball player reaches base 35% of the time. How many times can he expect to reach base in 850 at-bats?
Theoretical –
P(reaches base) = X/850
X/850 * .35 = 297.50
b. Jenna flips two pennies 105 times. How many times can she expect the coins to come up heads?
Experimental –
HH,HT,TT,TH
P ( 2 heads) = ¼
¼ * 105 = 105/4 = 25 ¼
P(1 head) = 1/2
½ * 105 = 105/2 = 52 1/2
c. Gil rolls a number cube 78 times. How many times can he expect to roll an odd number greater than 1?
Experimental
P ( 1, 3) = 2/6 = 1/3
1/3 * 78 = 26
a) ok, except how do you reach a base 1/2 a time ?
round off to 298
b) your wording is not clear. Do you want both coins to be heads, or just any head to be showing?
If you want both to be heads ---> prob = 1/4
number of double heads in 105 events
= 105/4 = appr 26 times
if you want a head to be shown, what we don't want is both tails
prob (some head) = 1 - 1/4 = 3/4
number of times this will happen = (3/4)(105) = appr 79 times
c) You are correct
Why is it 1 - 1/4 for the probability that one of the coins is sometimes heads? there are 4 outcomes and out of the 4 there are only 2 possibilities that the outcome is only heads. (2/4)
a shoebox holds a number of disks of the same size. there are 5 red, 6 white, and 7 blue disks. you pick out a disks, record its color, and return it to the box. if you repeat this process 250 times, how many times can you expect to pick either a red or white disk?
fvasv
a. The question asks how many times the baseball player can expect to reach base in 850 at-bats. To solve this question theoretically, we can use probability. The given information states that the player reaches base 35% of the time. We can set up the equation P(reaches base) = X/850, where X represents the number of times the player reaches base in 850 at-bats.
To solve for X, we can multiply both sides of the equation by 850, giving us X = 850 * 0.35. Evaluating this expression gives us X = 297.50.
Therefore, theoretically, the baseball player can expect to reach base 297.50 times in 850 at-bats.
b. The question asks how many times Jenna can expect the coins to come up heads when flipping two pennies 105 times. To solve this question experimentally, we need to consider the possible outcomes and their associated probabilities.
When flipping two pennies, the possible outcomes are: HH, HT, TT, and TH. The probability of getting 2 heads is 1 out of 4 possibilities, so P(2 heads) = 1/4.
To find the expected number of times 2 heads will occur, we can multiply the probability by the number of trials: 1/4 * 105 = 105/4 = 26 ¼.
Similarly, the probability of getting 1 head is 1/2. To find the expected number of times 1 head will occur, we can multiply the probability by the number of trials: 1/2 * 105 = 105/2 = 52 1/2.
Therefore, experimentally, Jenna can expect the coins to come up heads 26 ¼ times and 52 1/2 times when flipping two pennies 105 times.
c. The question asks how many times Gil can expect to roll an odd number greater than 1 when rolling a number cube 78 times. To solve this question experimentally, we need to consider the probability of rolling an odd number greater than 1.
When rolling a number cube, the possible outcomes are numbers 1 to 6. Out of these, the odd numbers greater than 1 are 3 and 5. So, the probability of rolling an odd number greater than 1 is 2 out of 6, which can be simplified to 1/3.
To find the expected number of times Gil will roll an odd number greater than 1, we can multiply the probability by the number of trials: 1/3 * 78 = 26.
Therefore, experimentally, Gil can expect to roll an odd number greater than 1 approximately 26 times when rolling a number cube 78 times.