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Probability Worksheets - Page 5

Probability Worksheets
  • Page 5
 41.  
Find the odds in favor of getting exactly 1 head when three coins are tossed.
a.
2 : 1
b.
5 : 3
c.
3 : 5
d.
1 : 2


Solution:

Sample space, S = {(H, H, H), (H, H, T), (H, T, H), (T, H, H), (H, T, T), (T, H, T), (T, T, H), (T, T, T)}

The odds in favor of getting exactly 1 head are 3 : 5
[Three outcomes are successes and 5 are failures.]


Correct answer : (3)
 42.  
A box contains 20 cards labeled 1 through 20. One card is drawn from it at random. Identify the event of drawing a card of an odd number.
a.
{11, 13, 15, 17, 19}
b.
{1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
c.
{1, 3, 5, 7, 9, 11, 13, 15, 17, 19}
d.
{1, 3, 5, 7, 9}


Solution:

Each outcome is a number of a card.

Let A be the event of drawing a card of an odd number.

A = {1, 3, 5, 7, 9, 11, 13, 15, 17, 19}

The event of drawing a card of an odd number is {1, 3, 5, 7, 9, 11, 13, 15, 17, 19}.


Correct answer : (3)
 43.  
A box contains 20 cards labeled 1 through 20 on them. One card is drawn from it at random. Write the event of drawing a multiple of 5.
a.
{5, 10, 15, 20}
b.
{5, 10}
c.
{5, 15}
d.
{1, 5, 10, 20}


Solution:

Each outcome is a number on a card.

Let B be the event of drawing a card whose number is a multiple of 5.

B = {5, 10, 15, 20}

The event of drawing a card whose number is a multiple of 5 is B = {5, 10, 15, 20}


Correct answer : (1)
 44.  
Fifteen cards labeled A through O are placed in a bag. The bag is shaken and one card is drawn at random. Write the event of drawing a consonant.
a.
{A, B, C, D, E, F, G, H, I, J}
b.
{B, C, D, F, G, H, J, K, L, M, N}
c.
{B, C, D, F, G, H, I, J, K, L, M}
d.
{A, E, I, O}


Solution:

Let Q be the event of drawing a consonant.

Q = {B, C, D, F, G, H, J, K, L, M, N}


Correct answer : (2)
 45.  
What is the probability of getting a red card from a 52-card deck?
a.
1 26
b.
1 2
c.
1 13
d.
1 4


Solution:

P(getting a red card) = 26 / 52 = 1 / 2
[There are 26 red cards.]


Correct answer : (2)
 46.  
If two dice are rolled, then what is the probability that the sum of the dots will be 8?
a.
5 36
b.
1 9
c.
1 6
d.
5 6


Solution:

The number of elements in the sample space, S = 6 × 6 = 36.

Let E be the event of getting the sum of dots is 8.

E = {(6, 2), (5, 3), (4, 4), (3, 5), (2, 6)}

The number of outcomes in E = 5

P(E) = Number of outcomes in the eventNumber of outcomes in the sample space

= 5 / 36


Correct answer : (1)
 47.  
Four cards are drawn from a bridge deck. What is the probability that all are diamonds?
a.
4 13
b.
11 4165
c.
1 4
d.
1 13


Solution:

The sample space, S is the set of all possible 4 card hands in a 52-card deck.

The number of outcomes in S is 52C4 = 52! / 4!48! = 270725

Let E be the event of getting 4 diamonds from 13 in the deck.

The number of outcomes in E is 13C4 = 13! / 4!9! = 715

P(E) = Number of outcomes in the eventNumber of outcomes in the sample space

= 715 / 270725 = 11 / 4165


Correct answer : (2)
 48.  
Two dice are rolled. What is the probability that the sum of the dots showing will be less than 8?
a.
1 2
b.
7 12
c.
13 18
d.
5 9


Solution:

The number of elements in sample space is 6 × 6 = 36.

Let E be the event of getting a sum less than 8 on the two dice.

E = {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (3, 1), (3, 2), (3, 3), (3, 4), (4, 1), (4, 2), (4, 3), (5, 1), (5, 2), (6, 1)}

Number of outcomes in E = 21

P(E) = Number of outcomes in the eventNumber of outcomes in the sample space

= 21 / 36 = 7 / 12


Correct answer : (2)
 49.  
There are 12 boys and 10 girls. If 7 of them are selected at random, what is the probability that 4 are boys and 3 are girls?
a.
7C312C4
b.
12C722C7
c.
(12C4)(10C3)22C7
d.
7 22


Solution:

Number of boys = 12

Number of girls = 10

Total number of students = 22

The number of ways of selecting 7 from 22 is 22C7.

So, the number of outcomes in sample space is 22C7.

Let E be the event of selecting 4 boys from 12 and 3 girls from 10.

Number of outcomes in E = 12C4 × 10C3

P(E) = Number of outcomes in the eventNumber of outcomes in the sample space

= (12C4)(10C3)22C7


Correct answer : (3)
 50.  
Two dice are rolled. What is the probability that both the dice show the same number of dots?
a.
1 6
b.
1
c.
1 2
d.
1 3


Solution:

The number of elements in sample space = 6 × 6 = 36

Let E be the event of getting the same number of dots on both the dice.

E = {(1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6)}

Number of outcomes in E = 6

P(E) = Number of outcomes in the eventNumber of outcomes in the sample space

= 6 / 36 = 1 / 6


Correct answer : (1)

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