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 to arrive at school are girls, we need to count how many times we see this outcome in the sample of 20 coin tosses. We can do this by looking at each set of three consecutive tosses and counting how many have exactly two tails (girls).
Out of the 20 sets of three tosses, there are 6 that have exactly two tails:
T H T (1st, 2nd, 3rd tosses)
T T H (2nd, 3rd, 4th tosses)
T H T (3rd, 4th, 5th tosses)
H T T (6th, 7th, 8th tosses)
T T H (11th, 12th, 13th tosses)
H H T (13th, 14th, 15th tosses)
Therefore, the experimental probability is 6/20, which simplifies to 3/10 or two-fifths.
Answer: C. two-fifths