Question 1 Determine the probability that either two heads o

Question #1: Determine the probability that either two heads or three heads will be thrown if six fair coins are tossed at once.

Question #2: Three standard 52-card decks of cards are used in a probability experiement. One card is drawn from each deck. Determine the probability that a diamond is drawn from the first deck, an ace is drawn from the second deck, and the king of hearts is drawn from the third deck of cards.

Solution

I)
Determine the probability that either two heads or three heads will be thrown if six fair coins are tossed at once

Six coins tossed at once sample sapce = 2^6 = 64
{hhhhhh, hhhhht, hhhhth, hhhhtt, hhhthh, hhhtht, hhhtth, hhhttt, hhthhh, hhthht, hhthth, hhthtt, hhtthh, hhttht, hhttth, hhtttt, hthhhh, hthhht, hthhth, hthhtt, hththh, hththt, hthtth, hthttt, htthhh, htthht, htthth, htthtt, httthh, htttht, htttth, httttt, thhhhh, thhhht, thhhth, thhhtt, thhthh, thhtht, thhtth, thhttt, ththhh, ththht, ththth, ththtt, thtthh, thttht, thttth, thtttt, tthhhh, tthhht, tthhth, tthhtt, tththh, tththt, tthtth, tthttt, ttthhh, ttthht, ttthth, ttthtt, tttthh, ttttht, ttttth, tttttt}

Getting 2 Heads in tossing coin 6 times = { hhtttt, hthttt,htthtt,htttht,htttth,thhttt,ththtt,thttht,thttth,tttthh,ttthth,ttthht,tthtth,tththt,tthhtt} = 15

Getting 3 Heads in tossing coin 6 times = { hhhttt, hhthtt, hhttht, hhttth, hthhtt,hththt,hthtth,htthht,htthth,httthh,thhhtt,thhtht,thhtth,ththht,ththth,thtthh,ttthhh,tththh,tthhth,tthhht } = 20

Grtting 2 HEads or 3 Heads = 15/64 + 20/64 = 35/64 = 0.5468