A campus radio station surveyed 500 students to determine th

A campus radio station surveyed 500 students to determine the types of music they like. The survey revealed that 211 like rock, 163 like country, and 122 like jazz. Moreover, 32 like rock and country, 31 like rock and jazz, 23 like country and jazz, and 12 like all three types of music. What is the probability that a randomly selected student likes country but not rock?

a) 0.3260

b) 0.2620

c) 0.3040

d) 0.2640

e) 0.2400

f) None of the above.

A 13 card hand is dealt from a well-shuffled standard 52-card deck. What is the probability that 6 red cards and 7 black cards are dealt?

a) 0.2785

b) 0.2385

c) 0.2885

d) 0.2355

e) 0.2985

f) None of the above.

What is the probability that 5 hearts are chosen if 7 cards are chosen from a well-shuffled deck of 52 playing cards?

a) 0.00000049

b) 0.00000026

c) 0.00712838

d) 0.00000962

e) 0.00000016

f) None of the above.

Solution

A)let take:as R is  like rock, C is like country, J is like jazz.  

from vene diagram:student likes country but not rock is

                                 131

and the probability that a randomly selected student likes country but not rock is:131/500=0.2620

   so answer is:b

B)13 card hand is dealt from a well-shuffled standard 52-card deck. What is the probability that 6 red cards and 7 black cards are dealt?

in 52 cards choose=13; 52C₁₃

    and select 6 cards from 26:26C₆

           select 7 cards from 26:26C₇

so required probabulity:(26C_{6 *}26C₇)/52C₁₃

                                                        230230*657800/635013559600

                                    =0.2385

ans is b

C)What is the probability that 5 hearts are chosen if 7 cards are chosen from a well-shuffled deck of 52 playing cards?

    it have 13 hearts

      select 5 cards from 13 hearts=13C₅

         remaing cards is (52-13)=39

      select 2 cards from 39=39C₂

                  so required probabulity is: 39C₂*13C₅  /52C₇   

                                            =1287*741/264385836=0.00712838

    ans) c