Probability & Statistics Homework 2: Theoretical Probability: A letter is randomly chosen from the w

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Math Statistics and Probability

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Answered by vanajareddy0426 a random 2 digit number is drawn (10-99) .total possibilities for 2 digit number= 90 1) Probability that being 32 P(32) = 901 =0.0111

2)total possible 2 digit odd numbers =45 p(odd number) = 9045 =0.5

3) possible numbers that are multiple of 5 = 18 P(multiple of 5) =9018 = 0.2 A letter is randomly selected from word candlestick 4) total letters = 11 Vowels in given word = a,e,i 3 vowel letters P(a vowel)= 3/11 =0.2727

5)in given word 1 n and 1 s are there.

They are mutually exclusive. p(n or s) = p(n)+p(s) = 2/11 = 0.1818

6)given word contains 2 c's.

So other than c possible ways are 11-2 =9 p(not c)=9/11 =0.8181

7)three coins are tossed.

Sample space {hhh,hht,hth,htt,thh,tht,tth,ttt} Total 8 possibilities.

P(2 heads) = 3/ 8 = 0.375

8) a month is choosen randomly.

Total months 12.

Months with less than 31 days are 5 months.

P( less than 31)=5/12 = 0.4167

9) Drawing a 9 or diamond from deck of cards.

Total cars 52 Number of 9 cards = 4 Number of diamond cards = 13 Number of 9 and diamonds = 1 P(9 or diamond) =(4+13-1)/52 =16/52 =0.3076

10) Credit cards have 3 digit lock.

For 3 digits total possible = 1000 Probability of number starting with 7 .

Password with starting 7 = 100 possibilities for next two places P(start 7) = 100/1000= 0.1

11) 2 dice are rolled.

Total possibilities 36.

Not getting doubles.

There are 6 chances for getting doubles (1,1)(2,2)(3,3)(4,4)(5,5)(6,6) P(not getting doubles = 1- (6/36) = 30/36 =5/6 =0.8333

12) having 14 Taylor Swift , 16 Meghan trainor, 17 Katy Perry songs.

Total 47 songs.

Next song playing is not Kerry is 47-17= 30 possible ways.

Probability = 30/47 = 0.6383

13) A dice is rolled ,than a coin tossed.

Probability of getting 5 than tail.

When a coin tossed 2 possible outcomes.head and tails with probability 1/2.

When is dice rolled probability of getting 5 is 1/6 P(5 and then tail )= (1/2)*(1/6) = 0.0833

14) a coin is tossed and a number from 0-10 is choosen .

Getting heads and number less than 4.

Probability of heads 1/2 Probability of number choosen is less than 4 = 3/10 P(heads then number less than 4) = (1/2)*(3/10) = 3/20 = 0.15 Step-by-step explanation

Compound probability is union or intersection of 2 events.

When 2 events one followed by other is occurring we calculate compound probability by multiplying each probability.