Question

A card is drawn from a deck of 52. Find the probability that the card is a heart, given that the card is red. That is, find P(heartlred). Tip: Restrict sample space. (2) Conditional probability: A card is drawn from a deck of 52. Find the probability that the card is a spade, given that the card is a king. That is, find P(spadelking). (3) Given the Sample Space:{1, 2, 3, 4, 5, 6), find the probability that the number is a 2, given that the number is even. That is, find P(2lthe number is even).

Answer 1

The probability of red heart is:
`(13)/(26) =(1)/(2)`

The probability of spadelking is:
`(1)/(4)`

The probability is:
`(1)/(3)`

Explanation:

Consider the provided information.

Part(A) Find the probability that the card is a heart, given that the card is red.

In a deck of 52 card we have 26 red cards in which 13 are heart.

Thus, the probability of red heart is:
`(13)/(26) =(1)/(2)`

Part(B) Find the probability that the card is a spade, given that the card is a king. That is, find P(spadelking).

In a deck of 52 card we have only 4 king cards out of which only 1 is spade king.

Thus, the probability of spadelking is:
`(1)/(4)`

Part(C) Given the Sample Space:{1, 2, 3, 4, 5, 6}, find the probability that the number is a 2, given that the number is even. That is, find P(2lthe number is even).

Consider the provided sample space, there are 3 even numbers in the provided sample space.

We need to find the probability that the number is a 2 given that the number is even.

Thus, the probability is:
`(1)/(3)`