Please show work and solve these 3 statistics questions 1) Hands of Cards a. Wha
ID: 3264741 • Letter: P
Question
Please show work and solve these 3 statistics questions
1) Hands of Cards
a. What’s the probability that a hand of 5 cards has at least 2 spades?
b. What’s the probability that a hand of 5 cards has at least 3 kings or at least 2 hearts?
2) Poker Odds
For this problem, you may look at https://en.wikipedia.org/wiki/Poker probability. It gives the probabilities for each of the 10 possible distinct poker hands to occur, using a standard 52-card deck with 4 suits and 13 cards of each suit. For each of the 10 possible hands, give the probability with which it would occur (in math terms like ( 39 5 ) ( 52 5 ) ) if you were instead using a 54-card deck with 6 suits and 9 cards of each suit. (include 5 of a kind as a possible hand, so 11 hands)
3) Bayes’ Theorem
Your smoke detector goes off with 99% probability if there is a fire, but there’s a 6% chance it goes off when there isn’t a fire. If 2.5% of houses catch on fire, what’s the probability that your house is on fire given that the smoke detector is going off?
Explanation / Answer
Ans:
P(goes off/fire)=0.99
P(goes off/not fire)=0.06
P(fire)=0.025
P(not fire)=0.975
Using Bayes theorm,
P(fire/goes off)=P(goes off/ fire)*P(fire)/[P(goes off/fire)*P(fire)+P(goes off/not fire)*P(not fire)]
=0.99*0.025/[0.99*0.025+0.06*0.975]
=0.02475/[0.02475+0.0585]
=0.02475/0.08325
=0.2973