Fenglin has a bag with 24 coins. Out of them, 21 are ordinary coins with equal chances of coming up heads and tails
when tossed, but 1 coin has tails on both faces, and 2 coins have heads on both faces.
Fenglin takes a random coin from the bag and tosses it without looking at which type of coin it is, checks which face
comes up, then places it back in the bag.
(a) If Fenglin tosses a random coin from the bag and it comes up heads, then the probability that this coin had heads
on both faces is
P(A) = 4/25
Syntax advice: Enter your answer using Maple syntax, and remember to use exact values.
Avoid decimal inputs, and do not approximate.
For example, if you have a probability of 0.5, enter 1/2
(b) If Fenglin tosses a random coin from the bag and it comes up tails, then the probability that this coin was ordinary
is
P(B) = 21/23
(c) Fenglin decides to try something different by taking all of the coins out of the bag and tosses each coin exactly
once on a table. The probability that Fenglin obtains at least 5 heads is
P(C) =
Syntax advice: In the above, you may want to recall the following Maple syntax:
$\binom{n}{k}$ may be written as binomial(n,k)
$\cdot$ the term $20!(2k+1)!$ may be written as 20!*(2*k+1)!
$\cdot$ the term $3^{40} (a + b)^{n+1}$ may be written as 3^40*(a+b)^(n+1)
