Jackson goes to the gym 0, 2, or 3 days per week, depending on work demands. The expected value of the number of days per week t

Answer:

Given that the frog jumps every 10 seconds

   (using digits from a random number table)

• It requires 7 jumps with 2 in the reverse direction (either left or right) for the frog to get off the board in 60 seconds.
• Alternatively, 3 jumps in the same direction will also lead to the frog being off the board.
• Furthermore, it would take 5 jumps with one in the opposite direction within the time limit of 60 seconds to leave the board.

Step-by-step explanation:

A frog positioned right at the center of a 5ft long board is 2.5 ft away from either edge.

Every 10 seconds, the frog jumps left or right.

If the frog's jumps are LLRLRL, it will remain on the board at the leftmost square.

If it jumps as LLRLL, it will jump off the board after fifty seconds.

Given that the frog jumps every 10 seconds

   (using digits from a random number table)

• It requires 7 jumps with 2 in reverse direction (either left or right) for the frog to get off the board in 60 seconds.
• Alternatively, 3 jumps in the same direction will also lead to the frog being off the board.
• Furthermore, it would take 5 jumps with one in the opposite direction within the time limit of 60 seconds to leave the board.

Complete Question

The complete question appears in the first uploaded image

Answer:

a) Yes, selecting 15 corresponds to a binomial experiment

b)

c)

d)

Regarding question a:

For an experiment to qualify as binomial

the trials have to be independent

each trial must yield one of two possible outcomes

Given that the selection of 15 individuals is random, we ascertain that the trials are independent and the outcomes are “either the individual saves for retirement or does not save for retirement.”

Therefore, we conclude that the selection of 15 people at random is indeed a binomial experiment.

In question b:

The probability that all selected adults do not save for retirement is mathematically modeled as

r = 15 implies all selected adults

n refers to the population size equating to 15

From the problem, p = 0.20

and q can be calculated as

=>

=>

Thus

Regarding question c:

The probability that exactly five of the selected adults do not save for retirement is mathematically modeled as

In relation to question d:

The probability that at least one of the selected adults opts not to save for retirement can be mathematically expressed as

Answer:

a) Ann has a 1/3 chance of winning in the first round

b) The chance of Ann winning for the first time in the fourth round is 8/81

c) The probability that Ann's first win occurs after the fourth round is 16/81

Step-by-step explanation:

a) Each strategy is played with a probability of 1/3. Given any strategy, there’s a 1/3 chance that Bill will choose the strategy that allows Ann to win. Consequently, the probability of Ann securing a victory in the first round (or any round) is

1/3 * 1/3 + 1/3 * 1/3 + 1/3 * 1/3 = 1/9 + 1/9 + 1/9 = 1/3.

Thus, the likelihood of Ann winning the initial round is 1/3.

b) The chances of Ann winning a round stand at 1/3; therefore, her chances of not winning are 2/3. This must happen three times before her first victory. Thus, the probability that Ann's first win occurs in the fourth round is

(2/3)³ * 1/3 = 8/81.

c) The first victory happens after the fourth round if she remains unsuccessful in the first four rounds, translating to a possibility of (2/3)⁴ = 16/81.