11.7 Probability  (Page 6/18)

 Page 6 / 18

Landing on a vowel

$\text{\hspace{0.17em}}\frac{1}{2}.\text{\hspace{0.17em}}$

Not landing on blue

Landing on purple or a vowel

$\text{\hspace{0.17em}}\frac{5}{8}.\text{\hspace{0.17em}}$

Landing on blue or a vowel

Landing on green or blue

$\text{\hspace{0.17em}}\frac{1}{2}.\text{\hspace{0.17em}}$

Landing on yellow or a consonant

Not landing on yellow or a consonant

$\text{\hspace{0.17em}}\frac{3}{8}.\text{\hspace{0.17em}}$

For the following exercises, two coins are tossed.

What is the sample space?

Find the probability of tossing two heads.

$\text{\hspace{0.17em}}\frac{1}{4}.\text{\hspace{0.17em}}$

Find the probability of tossing exactly one tail.

Find the probability of tossing at least one tail.

$\text{\hspace{0.17em}}\frac{3}{4}.\text{\hspace{0.17em}}$

For the following exercises, four coins are tossed.

What is the sample space?

Find the probability of tossing exactly two heads.

$\text{\hspace{0.17em}}\frac{3}{8}.\text{\hspace{0.17em}}$

Find the probability of tossing exactly three heads.

Find the probability of tossing four heads or four tails.

$\text{\hspace{0.17em}}\frac{1}{8}.\text{\hspace{0.17em}}$

Find the probability of tossing all tails.

Find the probability of tossing not all tails.

$\text{\hspace{0.17em}}\frac{15}{16}.\text{\hspace{0.17em}}$

Find the probability of tossing exactly two heads or at least two tails.

$\text{\hspace{0.17em}}\frac{5}{8}.\text{\hspace{0.17em}}$

For the following exercises, one card is drawn from a standard deck of $\text{\hspace{0.17em}}52\text{\hspace{0.17em}}$ cards. Find the probability of drawing the following:

A club

A two

$\text{\hspace{0.17em}}\frac{1}{13}.\text{\hspace{0.17em}}$

Six or seven

Red six

$\text{\hspace{0.17em}}\frac{1}{26}.\text{\hspace{0.17em}}$

An ace or a diamond

A non-ace

$\text{\hspace{0.17em}}\frac{12}{13}.\text{\hspace{0.17em}}$

A heart or a non-jack

For the following exercises, two dice are rolled, and the results are summed.

Construct a table showing the sample space of outcomes and sums.

1 2 3 4 5 6
1 (1, 1)
2
(1, 2)
3
(1, 3)
4
(1, 4)
5
(1, 5)
6
(1, 6)
7
2 (2, 1)
3
(2, 2)
4
(2, 3)
5
(2, 4)
6
(2, 5)
7
(2, 6)
8
3 (3, 1)
4
(3, 2)
5
(3, 3)
6
(3, 4)
7
(3, 5)
8
(3, 6)
9
4 (4, 1)
5
(4, 2)
6
(4, 3)
7
(4, 4)
8
(4, 5)
9
(4, 6)
10
5 (5, 1)
6
(5, 2)
7
(5, 3)
8
(5, 4)
9
(5, 5)
10
(5, 6)
11
6 (6, 1)
7
(6, 2)
8
(6, 3)
9
(6, 4)
10
(6, 5)
11
(6, 6)
12

Find the probability of rolling a sum of $\text{\hspace{0.17em}}3.\text{\hspace{0.17em}}$

Find the probability of rolling at least one four or a sum of $\text{\hspace{0.17em}}8.$

$\text{\hspace{0.17em}}\frac{5}{12}.$

Find the probability of rolling an odd sum less than $\text{\hspace{0.17em}}9.$

Find the probability of rolling a sum greater than or equal to $\text{\hspace{0.17em}}15.$

$\text{\hspace{0.17em}}0.$

Find the probability of rolling a sum less than $\text{\hspace{0.17em}}15.$

Find the probability of rolling a sum less than $\text{\hspace{0.17em}}6\text{\hspace{0.17em}}$ or greater than $\text{\hspace{0.17em}}9.$

$\text{\hspace{0.17em}}\frac{4}{9}.\text{\hspace{0.17em}}$

Find the probability of rolling a sum between $\text{\hspace{0.17em}}6\text{\hspace{0.17em}}$ and $\text{\hspace{0.17em}}9\text{,}\text{\hspace{0.17em}}$ inclusive.

Find the probability of rolling a sum of $\text{\hspace{0.17em}}5\text{\hspace{0.17em}}$ or $\text{\hspace{0.17em}}6.\text{\hspace{0.17em}}$

$\text{\hspace{0.17em}}\frac{1}{4}.\text{\hspace{0.17em}}$

Find the probability of rolling any sum other than $\text{\hspace{0.17em}}5\text{\hspace{0.17em}}$ or $\text{\hspace{0.17em}}6.\text{\hspace{0.17em}}$

For the following exercises, a coin is tossed, and a card is pulled from a standard deck. Find the probability of the following:

A head on the coin or a club

$\text{\hspace{0.17em}}\frac{3}{4}\text{\hspace{0.17em}}$

A tail on the coin or red ace

A head on the coin or a face card

$\text{\hspace{0.17em}}\frac{21}{26}\text{\hspace{0.17em}}$

No aces

For the following exercises, use this scenario: a bag of M&Ms contains $\text{\hspace{0.17em}}12\text{\hspace{0.17em}}$ blue, $\text{\hspace{0.17em}}6\text{\hspace{0.17em}}$ brown, $\text{\hspace{0.17em}}10\text{\hspace{0.17em}}$ orange, $\text{\hspace{0.17em}}8\text{\hspace{0.17em}}$ yellow, $\text{\hspace{0.17em}}8\text{\hspace{0.17em}}$ red, and $\text{\hspace{0.17em}}4\text{\hspace{0.17em}}$ green M&Ms. Reaching into the bag, a person grabs 5 M&Ms.

What is the probability of getting all blue M&Ms?

$\text{\hspace{0.17em}}\frac{C\left(12,5\right)}{C\left(48,5\right)}=\frac{1}{2162}\text{\hspace{0.17em}}$

What is the probability of getting $\text{\hspace{0.17em}}4\text{\hspace{0.17em}}$ blue M&Ms?

What is the probability of getting $\text{\hspace{0.17em}}3\text{\hspace{0.17em}}$ blue M&Ms?

$\frac{C\left(12,3\right)C\left(36,2\right)}{C\left(48,5\right)}=\frac{175}{2162}$

What is the probability of getting no brown M&Ms?

Extensions

Use the following scenario for the exercises that follow: In the game of Keno, a player starts by selecting $\text{\hspace{0.17em}}20\text{\hspace{0.17em}}$ numbers from the numbers $\text{\hspace{0.17em}}1\text{\hspace{0.17em}}$ to $\text{\hspace{0.17em}}80.\text{\hspace{0.17em}}$ After the player makes his selections, $\text{\hspace{0.17em}}20\text{\hspace{0.17em}}$ winning numbers are randomly selected from numbers $\text{\hspace{0.17em}}1\text{\hspace{0.17em}}$ to $\text{\hspace{0.17em}}80.\text{\hspace{0.17em}}$ A win occurs if the player has correctly selected $\text{\hspace{0.17em}}3,4,\text{\hspace{0.17em}}$ or $\text{\hspace{0.17em}}5\text{\hspace{0.17em}}$ of the $\text{\hspace{0.17em}}20\text{\hspace{0.17em}}$ winning numbers. (Round all answers to the nearest hundredth of a percent.)

can I see the picture
How would you find if a radical function is one to one?
how to understand calculus?
with doing calculus
SLIMANE
Thanks po.
Jenica
Hey I am new to precalculus, and wanted clarification please on what sine is as I am floored by the terms in this app? I don't mean to sound stupid but I have only completed up to college algebra.
I don't know if you are looking for a deeper answer or not, but the sine of an angle in a right triangle is the length of the opposite side to the angle in question divided by the length of the hypotenuse of said triangle.
Marco
can you give me sir tips to quickly understand precalculus. Im new too in that topic. Thanks
Jenica
if you remember sine, cosine, and tangent from geometry, all the relationships are the same but they use x y and r instead (x is adjacent, y is opposite, and r is hypotenuse).
Natalie
it is better to use unit circle than triangle .triangle is only used for acute angles but you can begin with. Download any application named"unit circle" you find in it all you need. unit circle is a circle centred at origine (0;0) with radius r= 1.
SLIMANE
What is domain
johnphilip
the standard equation of the ellipse that has vertices (0,-4)&(0,4) and foci (0, -15)&(0,15) it's standard equation is x^2 + y^2/16 =1 tell my why is it only x^2? why is there no a^2?
what is foci?
This term is plural for a focus, it is used for conic sections. For more detail or other math questions. I recommend researching on "Khan academy" or watching "The Organic Chemistry Tutor" YouTube channel.
Chris
how to determine the vertex,focus,directrix and axis of symmetry of the parabola by equations
i want to sure my answer of the exercise
what is the diameter of(x-2)²+(y-3)²=25
how to solve the Identity ?
what type of identity
Jeffrey
Confunction Identity
Barcenas
how to solve the sums
meena
hello guys
meena
For each year t, the population of a forest of trees is represented by the function A(t) = 117(1.029)t. In a neighboring forest, the population of the same type of tree is represented by the function B(t) = 86(1.025)t.
by how many trees did forest "A" have a greater number?
Shakeena
32.243
Kenard
how solve standard form of polar
what is a complex number used for?
It's just like any other number. The important thing to know is that they exist and can be used in computations like any number.
Steve
I would like to add that they are used in AC signal analysis for one thing
Scott
Good call Scott. Also radar signals I believe.
Steve
They are used in any profession where the phase of a waveform has to be accounted for in the calculations. Imagine two electrical signals in a wire that are out of phase by 90°. At some times they will interfere constructively, others destructively. Complex numbers simplify those equations
Tim
Is there any rule we can use to get the nth term ?
how do you get the (1.4427)^t in the carp problem?