﻿ Probability Worksheets - Page 7 | Problems & Solutions

Probability Worksheets - Page 7

Probability Worksheets
• Page 7
61.
Find the probability of selecting a yellow ball from the glass container.

 a. 2 out of 8 b. 3 out of 8 c. 7 out of 8 d. 3 out of 5

62.
A box contains dimes and pennies. Identify the probability of selecting a penny from the box.

 a. 3 out of 9 b. 5 out of 9 c. 6 out of 9 d. 3 out of 6

63.
What is the probability of picking a square from the figure shown?

 a. $\frac{1}{13}$ b. $\frac{7}{13}$ c. $\frac{2}{13}$ d. $\frac{11}{13}$

64.
Find the probability of picking a banana from the bag containing seven apples, two guavas, and two bananas as shown.

 a. 1 out of 2 b. 2 out of 11 c. 2 out of 9 d. 1 out of 10

65.
What is the probability of picking a yellow colored shape?
 Color of shapes Number of shapes Blue 5 Yellow 4 Pink 5 Brown 7 Green 5 Orange 5

 a. $\frac{1}{4}$ b. $\frac{1}{3}$ c. $\frac{4}{27}$ d. $\frac{4}{31}$

66.
When can the normal distribution be used as an approximation to the binomial distribution?
 a. $n$.$p$ = 5, $n$.$q$ = 5 b. $n$.$p$ ≤ 5, $n$.$q$ ≤ 5 c. $n$.$p$ > 5, $n$.$q$ < 5 d. $n$.$p$ ≥ 5, $n$.$q$ ≥ 5

Solution:

The normal distribution can be used as an approximation to the binomial distribution only when n.p and n.q are both greater than or equal to 5.
So, n.p ≥ 5 and n.q ≥ 5.

67.
Say whether the normal distribution can be used as an approximation to the binomial distribution shown here.
$n$ = 30 and $p$ = 0.5
 a. cannot be determined b. true c. false

Solution:

A binomial distribution can be approximated by the normal distribution if n.p ≥ 5 and n.q ≥ 5.

Given, n = 30 and p = 0.5

q = 1 - p = 0.5

n.p = 30 × 0.5 = 15 > 5

n.q = 30 × 0.5 = 15 > 5

We see that both n.p and n.q are ≥ 5. So, the normal distribution can be used as an approximation to the binomial distribution.

68.
Say whether the normal distribution can be used as an approximation to the binomial distribution shown here.
$n$ = 20 and $p$ = 0.8
 a. false b. true c. cannot be determined.

Solution:

A binomial distribution can be approximated by the normal distribution if n.p ≥ 5 and n.q ≥ 5.

Given, n = 20 and p = 0.8

q = 1 - p = 0.2

n.p = 20 × 0.8 = 16 > 5

n.q = 20 × 0.2 = 4 < 5

We see that n.p > 5 but n.q < 5. So, the normal distribution should not be used as an approximation to the binomial distribution.

69.
Which one of these is impossible to be picked from the box shown?

 a. circle b. rectangle c. square d. triangle