You want to determine the probability that in a family of 5 children, there will be more girls than boys. Which describes one trial of a simulation you could use to model this problem?
A.
Toss a coin 5 times and count the number of heads.
B.
Toss a 6-sided number cube 5 times and count the number of times you get a number less than 3.
C.
Generate 5 random numbers between 0 and 100 and count the number of prime numbers.
D.
Draw 5 cards at random from a standard 52-card deck, replacing each card after it is drawn and count the number of hearts. ( There are an equal number of hearts, spades, diamonds, and clubs in a deck.)
since prob(heads) = prob(tails) = 1/2
and prob(boy) = prob(girls) = 1/2
what do you think?
To determine the probability that in a family of 5 children, there will be more girls than boys, you need to simulate the scenarios and count the number of times the desired outcome occurs. Let's analyze each option to see which one works best:
A. Toss a coin 5 times and count the number of heads: This simulation is not appropriate for the problem because it only considers one outcome (heads or tails), whereas the problem is about comparing the number of girls and boys.
B. Toss a 6-sided number cube 5 times and count the number of times you get a number less than 3: This simulation is also not suitable because it only counts the occurrences of numbers less than 3, which doesn't relate to the problem of comparing the number of girls and boys.
C. Generate 5 random numbers between 0 and 100 and count the number of prime numbers: This simulation is not relevant to the problem, as it focuses on prime numbers rather than comparing the number of girls and boys.
D. Draw 5 cards at random from a standard 52-card deck, replacing each card after it is drawn, and count the number of hearts: This simulation is the most appropriate choice. Since there are an equal number of hearts, spades, diamonds, and clubs in the deck, drawing cards is comparable to the family having children. Counting the number of hearts in this simulation corresponds to the number of girls in the family. By repeating this trial multiple times and keeping track of the times there are more girls than boys, you can estimate the probability of this event occurring in a family of 5 children.
Therefore, option D, drawing 5 cards at random from a standard 52-card deck and counting the number of hearts, describes one trial of a simulation that can model this problem.