How to find a binomial probability

Find the probability of exactly three heads or at most three heads in ten fair coin tosses.

5 шагов

Эта статья пока не переведена на русский. Показана полная английская версия.

A fair coin is tossed ten times. What is the probability of getting exactly three heads? What about at most three heads? Let $X$ be the number of heads:

X \sim Bin (10, 0.5), P (X = 3), P (X \leq 3)

Here a head counts as a success: $N = 10$ is the number of trials, $p = 0.5$ is the probability of success on each trial, and $x = 3$ is the number of successes to check.

Find the exact and cumulative probabilities

Below each step is the screen you should see after pressing.

Next to each step is the screen you should see after pressing.

Step 1

Open the mode menu and tap Distribution.

Press:
Step 2

Tap the type name at the top of the screen to open the Select Type sheet.
Step 3

Tap Binomial PD. The parameter boxes appear with $x$ selected.
Step 4

Enter $3$ for $x$ and press the equals key, then enter $10$ for $N$ and press the equals key. Enter $0.5$ for $p$ . The answer updates to $0.117 1875$ as you type; you do not need to press the equals key after $p$ .

Press:
Step 5

Tap the type name again, then tap Binomial CD. The calculator keeps $x = 3$ , $N = 10$ and $p = 0.5$ and shows $0.171875$ .

Read and check the result

For this example, Binomial PD gives the probability of exactly three heads:

P (X = 3) = 0.1171875 = \frac{15}{128} .

Binomial CD includes zero, one, two or three heads:

P (X \leq 3) = 0.171875 = \frac{11}{64} .

The cumulative answer is larger because it includes the three-head outcome as well as the outcomes below it. The screen groups the digits in threes so long decimals are easier to read: $0.117 1875$ is $0.1171875$ .

If something goes wrong

A dashed box and Argument ERROR: check $p$ . For example, $p = 1.5$ causes this error. Tap the $p$ box, press AC once to empty it, then enter $0.5$ . A success probability must be between $0$ and $1$ .
The wrong type is selected: tap the type name and choose Binomial PD or Binomial CD again. Your $x$ , $N$ and $p$ values are kept.
A table opens after you press the equals key on p: this also stores the result in Ans. Tap the header's back arrow to return to the parameter boxes.

The fx-991EX screen in Binomial PD with x = 3, N = 10, p = 0.5 and P = 0.1171875.

Find a binomial probability on your fx-991EX calculator

Enter x = 3, N = 10 and p = 0.5 to find the chance of exactly three heads, then switch to Binomial CD for at most three.

Find the probability More guides

Find the exact and cumulative probabilities

Step 1

Step 2

Step 3

Step 4

Step 5

Read and check the result

If something goes wrong

Find a binomial probability on your fx-991EX calculator