Expected count = probability × number of tries. If it rains 3/10 of days, in 50 days expect 3/10 × 50 = 15 rainy days. An experiment gives an estimate: 24 shots in out of 80 means the estimated chance is 24/80 = 3/10.
Worked example
A basketball player makes 1/4 of free throws. Out of 12 free throws, about how many will the player make?
Answer:3 free throws
Expected count = probability × number of tries. 1/4 × 12 = 3 free throws. It is an estimate: real results vary a little.
For grown-ups: Experimental vs. theoretical (long-run relative frequency). Below: three problems to try with the worked answers, and a free printable sheet. Children can practise the same skill as a game, with no sign-up and no ads.
CCSS 7.SP.C.6
What this practises, for teachers
Practices experimental vs. theoretical (long-run relative frequency) (7.SP.C.6). A printable sheet with its answer key, worked answers on the page, no accounts.
The chance that a train is late is 1/5. Out of 20 trips, about how many trips will be late?
Show the answer and how
Answer:4 late trips
Expected count = probability × number of tries. 1/5 × 20 = 4 late trips. It is an estimate: real results vary a little.
15 out of 20 students surveyed ride a bike to school. Estimate the probability that a student chosen at random rides a bike. (Any fraction with the right value counts, so you do not have to reduce it.)
Show the answer and how
Answer:3/4
The experimental probability is the part that happened over all the tries: 15 out of 20 is 1520 = 34. Answer: 3/4.
A spinner lands on red 75% of the time. If it is spun 40 times, about how many times will it land on red?
Show the answer and how
Answer:30 times
Expected count = probability × number of tries. 75% × 40 = (75 ÷ 100) × 40 = 30 times. It is an estimate: real results vary a little.
The chance that a train is late is 1/5. Out of 30 trips, about how many trips will be late?
A spinner lands on red 3/10 of the time. If it is spun 30 times, about how many times will it land on red?
The chance that a train is late is 3/4. Out of 8 trips, about how many trips will be late?
A seed grows into a plant 1/10 of the time. If 60 seeds are planted, about how many will grow?
In 20 spins, a spinner landed on blue 15 times. Estimate the probability that it lands on blue. (Any fraction with the right value counts, so you do not have to reduce it.)
A baker checked 20 loaves and found 5 that were burnt. Estimate the probability that a loaf is burnt. (Any fraction with the right value counts, so you do not have to reduce it.)
A seed grows into a plant 1/5 of the time. If 20 seeds are planted, about how many will grow?
In 10 spins, a spinner landed on blue 8 times. Estimate the probability that it lands on blue. (Any fraction with the right value counts, so you do not have to reduce it.)
A baker checked 80 loaves and found 73 that were burnt. Estimate the probability that a loaf is burnt. (Any fraction with the right value counts, so you do not have to reduce it.)
In 100 spins, a spinner landed on blue 77 times. Estimate the probability that it lands on blue. (Any fraction with the right value counts, so you do not have to reduce it.)
A seed grows into a plant 40% of the time. If 40 seeds are planted, about how many will grow?
The chance of rain on any day is 0.8. In 200 days, about how many rainy days would you expect?