Probability
ICSE Class 7 · Mathematics · Chapter 22
What this chapter covers
- Chance in everyday life
- Words that describe how likely something is
- Experiments, trials and outcomes
- Tossing a coin and recording the results
- Throwing a die and tabulating its outcomes
- Comparing the die with the coin
- Strings of throws and the idea of randomness
- Using data to judge future events
Key points
- Chance describes whether something may or may not happen when the result cannot be known in advance.
- Events can be described as impossible, unlikely, equally likely, likely or certain.
- A random experiment, such as tossing a coin or throwing a die, can be repeated, has known outcomes, and gives an unpredictable result each time.
- A trial is one performance of the experiment; an outcome is one possible result; an event is one outcome or a group of outcomes.
- A coin has 2 equally likely outcomes; a die has 6 equally likely outcomes, if the coin or die is fair.
- Tally marks and frequency tables record how many times each outcome occurs; always check that the frequencies add up to the number of trials.
- Expected count for one outcome = number of trials ÷ number of equally likely outcomes.
- Actual counts wander from the expected counts in a few trials but settle closer as the number of trials grows.
- A single face of a die turns up less often than a single face of a coin, because the die has more outcomes to share its throws among.
- Random strings contain runs; a coin or die has no memory, so past results do not change the next result.
- Records of many past trials help you judge which outcome is most likely next, but never make it certain.
Questions answered
What is the difference between an impossible event and an unlikely event? Give one example of each.
An impossible event can never happen, such as getting an 8 on an ordinary die. An unlikely event probably will not happen but still can, such as getting the same number on a die five times in a row.
How many outcomes does tossing a coin have? How many does throwing a die have?
Tossing a coin has 2 outcomes, heads and tails. Throwing a die has 6 outcomes, 1, 2, 3, 4, 5 and 6.
Rohan tossed a fair coin 40 times and got 22 heads. Does this show that the coin is unfair? Explain.
No. About 20 heads were expected, and 22 is only 2 more. Small differences like this are normal in a small number of tosses.
A fair die is thrown 300 times. About how many times would you expect a 2 to appear?
There are 6 equally likely faces, so about 300 ÷ 6 = 50 times.
Make a frequency table for these 12 throws of a die: 5, 1, 5, 3, 6, 5, 2, 1, 4, 5, 6, 3.
Face 1: 2, face 2: 1, face 3: 2, face 4: 1, face 5: 4, face 6: 2. Total: 12.
In 90 tosses of a coin and 90 throws of a die, which would you expect to see more often: heads, or a 3 on the die? Give the expected counts.
Heads. Expected heads are 90 ÷ 2 = 45, while expected 3s are 90 ÷ 6 = 15.
Nisha says that after five tails in a row, the next toss is almost sure to be heads. Is she right?
No. A coin has no memory, so heads and tails remain equally likely on the next toss.
Find the longest run in this string of tosses: T H H T T T T T H T H H.
The longest run is five tails, TTTTT, from the 4th toss to the 8th.