Probability of not spinning a 7  = 1  - 1/10 = 9/10

Probability of tossing heads = 1/2

Probability of spinning a 3 = 1/10

So, the compound probability = 9/10 x 1/2 x 1/10 = 9/200.

I found an answer from math.stackexchange.com

What are the odds of getting heads 7 times in a row in 40 tries of ...

Let's count the number of ways not to get 7 heads in a row. ... in the second factor, the x (T) was chosen, then x3 (HHT), then x (T), then x2 (HT), to get ... To count the number of sequences of 40 flips that do not contain 7 consecutive heads, we  ...

For more information, see What are the odds of getting heads 7 times in a row in 40 tries of ...

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HW1 Solutions

Oct 5, 2016 ... 3. (2 pts.) Let A be the event that the first flip is a Heads. List all the outcomes ... For |D|, note that a outcome is not in D if the first and third flips are ... Comment: Note that if we place both coins on 7, then we need both rolls of.

For more information, see HW1 Solutions

I found an answer from www.khanacademy.org

Compound probability of independent events (video) | Khan Academy

You'll become familiar with the concept of independent events, or that one event ... But isn't it also true that the probability of six coins flips resulting in at least one T is very high? ... For instance if you roll a dice you can't get both three and four.

For more information, see Compound probability of independent events (video) | Khan Academy