Question

cards numbered from 1 through 31 are placed into a box and two cards are selected without replacement. Find the probability that both numbers selected are odd, given that their sum is even.

Find the probability that both numbers selected are odd, given that their sum is even.

Answer #1

Given that the sum of the 2 numbers is even, it is possible when either both the numbers are even or both are odd. Therefore number of ways to select 2 numbers such that the sum if even is computed as:

= Number of ways to select 2 even numbers + Number of ways to select 2 odd numbers

Probability that both numbers selected are odd given that the sum of two numbers is even is computed as:

= Number of ways to select two odd numbers / Total number of ways to get sum as even

**Therefore 0.5333 is the required probability
here.**

2. Two cards are selected from a deck of cards numbered 1 – 10.
Once a card is selected, it is not replaced. What is P(two even
numbers)?
a. 1/4
b.
2/9
c.
1/2
d. 1
3. In a fish tank there are 24 goldfish, 2 angel fish, and 5
guppies. If a fish is selected at random, find the probability that
it is a goldfish or an angelfish.
a. 26/31
b.
12/31 c.
24/2
d. 2/24

Suppose that a ball is selected at random from an urn with balls
numbered from 1 to 100, and without replacing that ball in the urn,
a second ball is selected at random. What is the probability
that:
1. The sum of two balls is below five.
2. Both balls have odd numbers.
3. Two consecutive numbers ar chosen, in ascending order

Consider picking three cards (without replacement) from five
cards marked with number 1 through 5, and observe the sequence.
(a) (2 pts) What is the total number of outcomes in the sample
space?
(b) (3 pts) What is the conditional probability the second card
is even given that the first card is even?
(c) (3 pts) What is the conditional probability the first two
cards are even given the third card is odd?
(d) (2 pts) Consider the following two...

One card is drawn from a deck of 20 cards numbered 1 through 20.
Find the probability of each scenario. (Enter your probabilities as
fractions.)
(a) The card drawn is odd and divisible by 4.
(b) The card drawn is odd or divisible by 4.
In a game where only one player can win, the probability that
Jack will win is 1/3 and the probability that Bill will win is 1/7.
Find the probability that one of them will win....

Two tickets are drawn from a box with 5 tickets numbered as
follows: 1,1,3,3,5. If the tickets are drawn with replacement, find
the probability that the first ticket is a 1 and the second ticket
is a 5. If the tickets are drawn without replacement, find the
probability that the first ticket is a 1 and the second ticket is a
3. If the tickets are drawn without replacement, find the
probability that the first ticket is a 1 and...

A box contains
11
balls numbered 1 through
11.
Two balls are drawn in succession without replacement. If the
second ball has the number 4 on it, what is the probability that
the first ball had a smaller number on it? An even number on
it?
The probability that the first ball had a smaller number is
_____.
(Type a fraction. Simplify your answer.)
The probability that the first ball had an even number is
____.
(Type a fraction. Simplify...

You have ten different cards: the Ace through 5 of spades and
clubs. Three cards are selected at random without replacement. What
is the probability of the sum of the numbers on the
three cards is divisible by 7 (use 1 fore Ace)

If 2 cards are selected from a deck of 52 cards
without replacement, find the probability of both are the same
color

Problem 31: Two cards are dealt from an ordinary deck of 52
cards. This means that two cards are sampled uniformly at random
without replacement.
a What is the probability that both cards are aces and one of
them is the ace of spaces?
b What is the probability that at least one of the cards is an
ace?

Let n be in N. Two packs of cards each containing cards numbered
1 to n are shuffled and placed on the table. One by one, two cards
are simultaneously turned over from the top of the packs. What is
the probability that at some point the two revealed cards have the
same number?

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