Eight children in a swimming race are John, Iain,
Hans, Ivan, Giovanni, Beth, Liz and Elisa.
They are put in lanes 1 to 8 randomly.
What is the probability that Beth, Liz or Elisa
is in lane 1?
What is 3/8 ?
To find the probability that either Beth, Liz, or Elisa is in lane 1, we first need to determine the total number of possible outcomes. Since there are 8 children and 8 lanes, there are 8! (8 factorial) ways to arrange the children in the lanes.
Next, we need to find the number of favorable outcomes, i.e., the number of arrangements where either Beth, Liz, or Elisa is in lane 1. Since there are three children (Beth, Liz, and Elisa) who could potentially be in lane 1, and there are 7 remaining lanes for the other children to be placed in, we can calculate the number of favorable outcomes using the following formula:
Number of favorable outcomes = 3! x 7!
The number 3! represents the number of ways that Beth, Liz, and Elisa can be arranged among themselves in lane 1 (which is 3 factorial), while the number 7! represents the number of ways that the remaining 7 children can be arranged in the remaining 7 lanes.
Finally, we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes:
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = (3! x 7!) / 8!
To determine the exact value for the probability, we need to evaluate this expression using the factorial notation:
Probability = (3 x 2 x 1 x 7 x 6 x 5 x 4 x 3 x 2 x 1) / (8 x 7 x 6 x 5 x 4 x 3 x 2 x 1)
Calculating and simplifying this expression, we get:
Probability = 3/8
Therefore, the probability that either Beth, Liz, or Elisa is in lane 1 is 3/8.