A school has an equal number of boys and girls. You use a coin to simulate the first three students to arrive at school each day, where “heads” represents a boy and “tails” represents a girl. The table below shows a sample of 20 coin tosses
T H T
T T T
T H T
H T H
H H H
T T T
H T T
H H T
T H T
T T T
T T H
T H T
H H T
H H H
H T H
T H T
H H T
T T T
H H H
T H T
Find the experimental probability that the first three students to arrive at school are boys.
A. Start Fraction 3 over 20 End Fraction
B. one-fifth
C. start fraction 3 over 10 end fraction
D. one-fourth.
To find the experimental probability of the first three students being boys, we need to count how many times the coin toss resulted in "heads-heads-heads" (representing three boys). Looking at the table, we can see that this happened three times.
Therefore, the experimental probability is:
Start Fraction 3 over 20 End Fraction
So the answer is A.
3. Briefly, discuss the acquisition and disposal of a member’s interest in a Close Corporation in light of case, Davidson v Cough N.O. and Others (41962/2021) [2022] ZAGPJHC
Davidson v Cough N.O. and Others (41962/2021) [2022] ZAGPJHC is a recent South African court case that dealt with the acquisition and disposal of a member's interest in a close corporation. The case involved a dispute between two members of a close corporation, where one member wanted to dispose of their interest in the corporation and the other member objected to the sale.
The court confirmed that the rights and obligations of the members of a close corporation are governed by the corporation's founding documents, such as its shareholders' agreement and memorandum of incorporation. These documents can provide for the circumstances under which a member can dispose of their interest, and the process to be followed in such a case.
In this particular case, the court found that the shareholders' agreement did not prevent a member from disposing of their interest in the close corporation, but it required the consent of the other members for the transfer to be effective. The court held that the other member's objection was unreasonable and lacked a valid basis, and therefore ordered the transfer to proceed.
Overall, this case highlights the importance of having clear and comprehensive founding documents for a close corporation, which can set out the process for the acquisition and disposal of a member's interest. It also demonstrates that any objections to a transfer must be reasonable and based on valid grounds.
3. Briefly, discuss the acquisition and disposal of a member’s interest in a Close Corporation in light of case, Davidson v Cough N.O. and Others (41962/2021) [2022] ZAGPJHC
Davidson v Cough N.O. and Others (41962/2021) [2022] ZAGPJHC is a South African court case that dealt with the acquisition and disposal of a member's interest in a close corporation. The court confirmed that the rights and obligations of the members of a close corporation are determined by the corporation's founding documents, such as its shareholders' agreement and memorandum of incorporation, which can provide for the circumstances under which a member can dispose of their interest, and the process to be followed in such a case.
In this case, the shareholders' agreement did not prohibit a member from disposing of their interest in the close corporation, but any transfer required the consent of the other members to be effective. Furthermore, the court found that the transfer could not be unreasonably withheld. The member objecting to the transfer, in this case, lacked a valid basis for their objection and was deemed to be acting unreasonably.
Therefore, this case highlights the importance of having clear and comprehensive founding documents for a close corporation, which can set out the process and requirements for the acquisition and disposal of a member's interest, and the obligations and rights of the members. It also emphasizes that objections to a transfer must have a valid basis and must not be unreasonable.
To find the experimental probability that the first three students to arrive at school are boys, we need to count the number of times the coin resulted in "heads" three times in a row.
From the given sample of 20 coin tosses, we can count the number of times the coin resulted in "heads" three times in a row:
HHH (1st toss: H, 2nd toss: H, 3rd toss: H)
HHH (1st toss: H, 2nd toss: H, 3rd toss: H)
HHH (1st toss: H, 2nd toss: H, 3rd toss: H)
So, we have three instances where the first three students to arrive at school were boys.
The total number of tosses is 20.
The experimental probability is calculated by dividing the number of successes (boys) by the total number of trials (tosses):
Experimental probability = Number of successes / Total number of trials
= 3 / 20
Therefore, the experimental probability that the first three students to arrive at school are boys is:
A. Start Fraction 3 over 20 End Fraction
To find the experimental probability that the first three students to arrive at school are boys, we need to calculate the number of times the coin toss resulted in "heads" (representing boys) in the given sample.
Looking at the table, we can count the number of times "H" (heads) appears in the first three positions. Let's count:
T H T - This is a boy
T T T - No boys
T H T - This is a boy
H T H - This is a boy
H H H - This is a boy
T T T - No boys
H T T - This is a boy
H H T - This is a boy
T H T - This is a boy
T T T - No boys
T T H - This is a boy
T H T - This is a boy
H H T - This is a boy
H H H - This is a boy
H T H - This is a boy
T H T - This is a boy
H H T - This is a boy
T T T - No boys
H H H - This is a boy
T H T - This is a boy
From the count above, we can see that the coin toss resulted in "heads" (representing boys) 12 times out of the 20 given coin tosses.
Therefore, the experimental probability of the first three students being boys is Start Fraction 12 over 20 End Fraction, which simplifies to Start Fraction 3 over 5 End Fraction.
So the correct answer is A) Start Fraction 3 over 20 End Fraction.