Question

A box contains 4 chocobars and 4 ice creams. tom eats 3 of them, by randomly choosing. what is the probability of choosing 2 chocobars and 1 icecream

Answer 1

Answer: $\dfrac{3}{7}$

Step-by-step explanation:

Given: The number of chocobars : 4

The number of ice-creams : 4

Total number of items : $4+4=8$

Now, if Tom eats 3 of them, by randomly choosing.Then the probability of choosing 2 chocobars and 1 ice-cream is given by :-

$\text{P(2 chocobars, 1 ice-cream)}=\dfrac{^4C_2\times ^4C_1}{^8C_3}$

$\dfrac{\frac{4!}{2!(4-2)!}\times4}{\frac{8!}{3!(8-3)!}}\\\\\\=\dfrac{3}{7}$

Hence, the probability of choosing 2 chocobars and 1 ice-cream =  $\dfrac{3}{7}$

Answer 2

the probability of choosing 2 chocobars and 1 icecream is 3/7

Further explanation

The probability of an event is defined as the possibility of an event occurring against sample space.

$\large { \boxed {P(A) = \frac{\text{Number of Favorable Outcomes to A}}{\text {Total Number of Outcomes}} } }$

Permutation ( Arrangement )

Permutation is the number of ways to arrange objects.

$\large {\boxed {^nP_r = \frac{n!}{(n - r)!} } }$

Combination ( Selection )

Combination is the number of ways to select objects.

$\large {\boxed {^nC_r = \frac{n!}{r! (n - r)!} } }$

Let us tackle the problem.

A box contains 4 chocobars and 4 ice creams.

There are a total of 8 objects

The probability of choosing the first chocobars P(C₁) is:

$P(C_1) = \frac{4}{8}$

The probability of choosing the second chocobars P(C₂) is:

$P(C_2) = \frac{3}{7}$

The probability of choosing the icecreams P(I) is:

$P(I) = \frac{4}{6}$

The probability of choosing 2 chocobars and 1 icecream is:

$P(C_1 , C_2 , I) = \frac{4}{8} \times \frac{3}{7} \times \frac{4}{6} = \frac{1}{7}$

$P(C_1 , I , C_2) = \frac{4}{8} \times \frac{4}{6} \times \frac{3}{7} = \frac{1}{7}$

$P(I , C_1 , C_2) = \frac{4}{6} \times \frac{4}{8} \times \frac{3}{7} = \frac{1}{7}$

$\large {\boxed {\therefore P(2C ~ \text{and} ~ I) = \frac{1}{7} + \frac{1}{7} + \frac{1}{7} = \frac{3}{7}} }$

Learn more

• Different Birthdays : https://brainly.com/question/7567074
• Dependent or Independent Events : https://brainly.com/question/12029535
• Mutually exclusive : https://brainly.com/question/3464581

Answer details

Grade: High School

Subject: Mathematics

Chapter: Probability

Keywords: Probability , Sample , Space , Six , Dice , Die , Binomial , Distribution , Mean , Variance , Standard Deviation