Question

Here are five number cards.
19
13
10
14
22
Two of the five cards are picked at random.
Work out the probability that the total of the two numbers is more than 32

Answer 1

Possible ways to get >32:
19 , 14
14, 19
18,22
22, 19
13,22
22,13
14, 22
22,14

That is 8 ways
Total number of permutations of 2 cards from 5
= 5P2
= 5!/3!
= 20
So required probability
= 8/20
= 2/5.

Answer 2

The probability that the total of the two numbers is more than 32 = $\frac{2}{5}$

What is probability?

"Probability is a branch of mathematics which deals with finding out the likelihood of the occurrence of an event."

Formula of the probability of an event A is:

P(A) = n(A)/n(S)

where,  n(A) is the number of favorable outcomes, n(S) is the total number of events in the sample space.

What is the formula of combination?

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

For given question,

We have been given five number cards.

Two of the five cards are picked at random.

Using combination formula the possible number of outcomes would be,

$^5C_2\\\\=\frac{5!}{2!(5-2)!} \\\\=10$

So, n(S) = 10

Let event A : the total of the two numbers is more than 32

A = {(19, 14), (19, 22), (13, 22), (14, 22)}

So, n(A) = 4

Using the formula for probability,

$\Rightarrow P(A)=\frac{n(A)}{n(S)} \\\\\Rightarrow P(A)=\frac{4}{10}\\\\\Rightarrow P(A)=\frac{2}{5}$

Therefore, the probability that the total of the two numbers is more than 32 = $\frac{2}{5}$

Learn more about probability here:

brainly.com/question/11234923

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