Question

Design for safety probability homework 1) If you have 2 dice, what is the probability of rolling a 3 and 2) If you have 2 dice, what is the probability of rolling a 4 and 3) If you have 2 dice, what is the probability of rolling a 2 ora 4) If you have a deck of cards, what is the probability of 5) If you have a deck of cards, what is the probability of a 1 or 3 4 drawing a spade or a red card with 1 draw drawing a spade or a red card with 2 draws without replacement 6) If you have a deck of cards, what is the probability of drawing a royal flush (10,J,Q,K,A of the same suit) (no replacement) 7) If you have a deck of cards, what is the probability of drawing an ace or a black card 8) If three events, A, B and C need to all occur for a failure and, P(A)-0.2, P(B)-0.1, and P(C)-0.05, calculate the probability of failure 9) If any of three events, A, B and C need occur for a failure and, P(A)-0.2, P(B)-0.1, and P(C)-0.05, calculate the probability of failure if A, B, and C are mutually exclusive 10) If any of three events, A, B and C need occur for a failure and, P(A)-0.2, P(B)-0.1, and P(C)-0.05, calculate the probability of failure if A, B, and C are not mutually exclusive

Answer 1

In a single roll of a dice probability of getting any number out of 1,2,3,4,5,6 is 1/6

1)If we have 2 dice then the probability of rolling a 3 and a 4 is

if we roll 2 dice then possible outcomes are

(1,1)(1,2)(1,3)(1,4)(1,5)(1,6)

(2,1)(2,2)(2,3)(2,4)(2,5)(2,6)

(3,1)(3,2)(3,3)(3,4)(3,5)(3,6)

(4,1)(4,2)(4,3)(4,4)(4,5)(4,6)

(5,1)(5,2)(5,3)(5,4)(5,5)(5,6)

(6,1)(6,2)(6,3)(6,4)(6,5)(6,6)

Probability(rolling 3 and a 4)=2/36=1/18

2)probability of rolling 4 and a 1 or 3

if we roll 2 dice then possible outcomes are

(1,1)(1,2)(1,3)(1,4)(1,5)(1,6)

(2,1)(2,2)(2,3)(2,4)(2,5)(2,6)

(3,1)(3,2)(3,3)(3,4)(3,5)(3,6)

(4,1)(4,2)(4,3)(4,4)(4,5)(4,6)

(5,1)(5,2)(5,3)(5,4)(5,5)(5,6)

(6,1)(6,2)(6,3)(6,4)(6,5)(6,6)

Probability of rolling 4 and a 1 or 3 =4/36=1/9

3)If we have two dice then the probability of rolling a 2 or a 4

if we roll 2 dice then possible outcomes are

(1,1)(1,2)(1,3)(1,4)(1,5)(1,6)

(2,1)(2,2)(2,3)(2,4)(2,5)(2,6)

(3,1)(3,2)(3,3)(3,4)(3,5)(3,6)

(4,1)(4,2)(4,3)(4,4)(4,5)(4,6)

(5,1)(5,2)(5,3)(5,4)(5,5)(5,6)

(6,1)(6,2)(6,3)(6,4)(6,5)(6,6)

Probability(rolling a 2 or a 4)=20/36=5/9

4)In a deck of cards there are total 52 number of cards out of which 26 are red cards and 26 are black

Deck of cards is divided into 4 parts as spade,club,hearts and diamonds with 13 card each

Probability of drawing spade or a red card with 1 draw=(13/52+26/52)=(1/4+1/2)=3/4