5. Binomial Distribution & Discrete Random Variables
Hypergeometric Distribution
Struggling with Statistics?
Join thousands of students who trust us to help them ace their exams!Watch the first videoMultiple Choice
Find the probability of drawing a hand of 5 cards from a standard deck that contains exactly 2 hearts.
A
B
C
D
Verified step by step guidance1
Step 1: Understand the problem. You are tasked with finding the probability of drawing a hand of 5 cards from a standard deck of 52 cards that contains exactly 2 hearts. A standard deck has 13 hearts and 39 non-hearts.
Step 2: Use the combination formula to calculate the number of ways to choose 2 hearts from the 13 available hearts. The formula for combinations is C(n, k) = n! / (k!(n-k)!), where n is the total number of items, and k is the number of items to choose.
Step 3: Similarly, calculate the number of ways to choose the remaining 3 cards from the 39 non-hearts using the same combination formula.
Step 4: Multiply the results from Step 2 and Step 3 to find the total number of favorable outcomes (hands with exactly 2 hearts).
Step 5: Divide the total number of favorable outcomes by the total number of possible 5-card hands from the deck, which is calculated as C(52, 5). This gives the probability of drawing a hand with exactly 2 hearts.
5:15mWatch next
Master Introduction to the Hypergeometric Distribution with a bite sized video explanation from Patrick
Start learningRelated Videos
Related Practice
