Answer:
1st One goes to the third one
2nd one goes to the 1st one
3rd one goes to the 4th one
and the 4th one goes to the 2nd one
Answer:
a) 9%
, not unusual
b) 42.4%
c) 48.4%
d) 11.1%
, 44.4%
, 44.4%
Step-by-step explanation:
We have the following information from the statement:
n = 12
r = 4
a)
P (likebothofthem) = P (likefirstsong) * P (likesecondsong)
P = 4/12 * 3/11
P = 0.09 = 9%
The probability is not unusual, unusual is considered less than 0.05 or 5%
b)
P (likeneither) = P (notlikefirstsong) * P (notlikesecondsong)
P = 8/12 * 7/11
P = 0.424 = 42.4%
c) P (likeexactlyoneofthem) = P (firstsongliked) * P (secondsongnotliked) + P (firstsongnotliked) * P (secondsongliked)
P = (4/12 * 8/11) + (8/12 * 4/11)
P = 0.484 = 48.4%
d)
a)
P (likebothofthem) = P (likefirstsong) * P (likesecondsong)
P = 4/12 * 4/12
P = 0.111 = 11.1%
The probability is not unusual, unusual is considered less than 0.05 or 5%
b)
P (likeneither) = P (notlikefirstsong) * P (notlikesecondsong)
P = 8/12 * 8/12
P = 0.444 = 44.4%
c) P (likeexactlyoneofthem) = P (firstsongliked) * P (secondsongnotliked) + P (firstsongnotliked) * P (secondsongliked)
P = (4/12 * 8/12) + (8/12 * 4/12)
P = 0.444 = 44.4%
<em>Without</em> using a truth table:
(<em>p</em> ⇒ <em>q</em>) ∨ <em>q</em> ⇔ (¬<em>p</em> ∨ <em>q</em>) ∨ <em>q</em> ⇔ ¬<em>p</em> ∨ <em>q</em> ⇔ <em>p</em> ⇒ <em>q</em>
<em />
<em>With</em> a table:
<em>p</em> … <em>q</em> … <em>p</em> ⇒ <em>q</em> … (<em>p</em> ⇒ <em>q</em>) ∨ <em>q</em>
T … T … T … T
T … F … F … F
F … T … T … T
F … F … T … T
