Binomial Probabilities

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Questions 1-2

179

Question 1.

What is the value of 6!?

Correct. 6! = 6 x 5 x 4 x 3 x 2 x 1 = 720.

Incorrect. 6! = 6 x 5 x 4 x 3 x 2 x 1 = 720.

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Question 2.

How many ways are there to get 6 heads in 10 flips of a coin?

210

1,000,000

Correct. There are

$\begin{bmatrix}10 \\6 \end{bmatrix}$ possible ways. This is

$\frac{10!}{6!(10-6)!}$ = 210.

Incorrect. There are

$\begin{bmatrix}10 \\6 \end{bmatrix}$ possible ways. This is

$\frac{10!}{6!(10-6)!}$ = 210.

Try again.

Question 3

416

Question 3.

If n = 8 and p = 0.6, what is P(X = 6)?

4*7*0.6⁶*0.4²

8*6*0.6⁶*0.4²

8*7*0.6⁶*0.4²

0.6⁶*0.4²

Correct. The probability is

$\begin{bmatrix}8 \\6 \end{bmatrix}$ 0.6⁶(1-0.6)²=

$\dfrac{8\,x\, 7\, x\, 6\, x\, 5\, x\, 4\, x\, 3\, x\, 2\, x\, 1}{6\, x\, 5\, x\, 4\, x\, 3\, x\, 2\, x\, 1(2\, x\, 1)}\,0.6(0.4)$ ². Note that 6\,x\,5\,x\,4\,x\,3\,x\,2\,x\,1 cancels from the numerator and denominator and the leftover 2 in the denominator cancels with the 8 to leave 4.

Incorrect. The probability is

$\begin{bmatrix}8 \\6 \end{bmatrix}$ 0.6⁶(1-0.6)²=

$\dfrac{8 \,x \,7 \,x \,6 \,x \,5 \,x \,4 \,x \,3 \,x \,2 \,x \,1}{6 \,x \,5 \,x \,4 \,x \,3 \,x \,2 \,x \,1(2 \,x \,1)}\,0.6(0.4)$ ². Note that 6x5x4x3x2x1 cancels from the numerator and denominator and the leftover 2 in the denominator cancels with the 8 to leave 4.

Try again.

StatTutor Lesson - Binomial Probabilities

Questions 1-2

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Question 2.

Question 3

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Questions 4-7

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Question 7.