There are 10 coins. 9 are fair and one is double-headed.
(1) randomly choose a coin, flip it, and put it back. what's the probability of getting 5 heads in 5 flips?

0.050328

Step-by-step explanation:

Given that there are 10 coins, out of which 9 are fair and one is double headed.

P(selecting fair coin) = 0.9 and P(selecting double headed coin) = 0.1

P(H/fair coin)= 0.5 and P(H/doube headed ) = 1

Probability of getting in 1 toss head = Prob of selecting fair coin and getting head+ Prob of selecting double headed and getting head

=

This will be constant p for 10 trials going to be done because coin is replaced each time.

Also there are only two outcomes

X no of heads in 5 flips is Binomial with (5, 0.55)

P(x=5) = Reqd probability

=

6mm^3 or .6cm^3

      216

      /   \

  36     6

  /   \     /

6     6   6

factor trees are nice.