Question

Dr. Stats plans to toss a fair coin $10,000$ times in the hope that it will lead him to a deeper understanding of the laws of probability. Which of the following statements is true?

(a) It is unlikely that Dr. Stats will get more than $5000$ heads.

(b) Whenever Dr. Stats gets a string of 15 tails in a row, it becomes more likely that the next toss will be a head.

(c) The fraction of tosses resulting in heads should be close to$1/2$

(d) The chance that the$100th$ toss will be a head depends somewhat on the results of the first $99$ tosses.

(e) All of the above statements are true.

Short answer

The correct option is (c) .

Step-by-step solution

Step 1. Given

$10,000$ times a coin has been tossed. The coin is in good condition.

Step 2. Concept

The probability of an event=$\frac{numberoffavourableoutcomes}{totalnumberofoutcomes}$

Step 3. Calculation

The coin is in good condition. As a result, both heads and tails have an equal chance of occurring. As a result, half of the heads and tails should be expected. There would be $5000$ heads and $5000$ tails in all. The chance of receiving a head is: $P\left(Head\right)=\frac{5000}{10000}=\frac{1}{2}$

As a result, the fraction of people that obtain heads is $12$

As a result, the best solution is (e).