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 exactly two out of the first three students to arrive at school are girls.
A. one-fifth
B. one-fourth
C. two-fifths
D. one-eighth.
To find the experimental probability that exactly two out of the first three students are girls, we need to count the number of times we got "tails" exactly twice in the first three coin tosses. Looking at the table, we see that this happened four times:
T H T (the first two tosses are tails)
T T H (the last two tosses are tails)
T H T
T H T
Out of 20 total tosses, the experimental probability of getting exactly two tails in the first three tosses is 4/20 = 1/5.
Therefore, the answer is A. one-fifth.
To find the experimental probability that exactly two out of the first three students to arrive at school are girls, we need to count the number of times this event occurs and divide it by the total number of trials.
Looking at the table, we can see that the event "exactly two out of the first three students are girls" occurs 5 times (highlighted below):
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**
Out of the 20 trials, this event occurs 5 times.
Therefore, the experimental probability is 5/20 = 1/4.
So the answer is B. One-fourth.