MATH SOLVE

2 months ago

Q:
# 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).

Accepted Solution

A:

Answer:The probability of red heart is: [tex]\frac{13}{26} =\frac{1}{2}[/tex]The probability of spadelking is: [tex]\frac{1}{4}[/tex]The probability is: [tex]\frac{1}{3}[/tex]Step-by-step 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: [tex]\frac{13}{26} =\frac{1}{2}[/tex]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: [tex]\frac{1}{4}[/tex]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: [tex]\frac{1}{3}[/tex]